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In [[mathematics]], in the field of [[abstract algebra]], the '''structure theorem for finitely generated modules over a principal ideal domain''' is a generalization of the [[fundamental theorem of finitely generated abelian groups]] and roughly states that finitely generated modules can be uniquely decomposed in much the same way that integers have a [[prime factorization]]. The result provides a simple framework to understand various canonical form results for square matrices over fields.
{{Probability distribution|
  name      = Shifted Gompertz|
  type      =density|
  pdf_image  =[[File:Shiftedgompertz distribution PDF new.png|325px|Probability density plots of shifted Gompertz distributions]]|
  cdf_image  =[[File:Shiftedgompertz distribution CDF new.png|325px|Cumulative distribution plots of shifted Gompertz distributions]]|
  parameters =<math>b>0</math> [[scale parameter|scale]] ([[real number|real]])<br/><math>\eta>0</math> [[shape parameter|shape]] (real)|
  support    =<math>x \in [0, \infty)\!</math>|
  pdf        =<math>b e^{-bx} e^{-\eta e^{-bx}}\left[1 + \eta\left(1 - e^{-bx}\right)\right]</math>|
  cdf        =<math>\left(1 - e^{-bx}\right)e^{-\eta e^{-bx}}</math>|
  mean      =<math>(-1/b)\{\mathrm{E}[\ln(X)] - \ln(\eta)\}\,</math>
where <math>X = \eta e^{-bx}\,</math> and
<math>\begin{align}\mathrm{E}[\ln(X)] =& [1 {+} 1 / \eta]\!\!\int_0^\eta \!\!\!\! e^{-X}[\ln(X)]dX\\ &- 1/\eta\!\! \int_0^\eta \!\!\!\! X e^{-X}[\ln(X)] dX \end{align}</math>|
  median    =|
  mode      = <math>0 \text{ for }0 < \eta \leq 0.5</math><br/> <math>(-1/b)\ln(z^\star)\text{, for } \eta > 0.5</math><br/><math>\text{ where }z^\star = [3 + \eta - (\eta^2 + 2\eta + 5)^{1/2}]/(2\eta)</math>|
  variance  =<math>(1/b^2)(\mathrm{E}\{[\ln(X)]^2\} - (\mathrm{E}[\ln(X)])^2)\,</math>
where <math>X = \eta e^{-bx}\,</math> and <math>\begin{align}\mathrm{E}\{[\ln(X)]^2\} =& [1 {+} 1 / \eta]\!\!\int_0^\eta \!\!\!\! e^{-X}[\ln(X)]^2 dX\\ &- 1/\eta \!\!\int_0^\eta \!\!\!\! X e^{-X}[\ln(X)]^2 dX \end{align}</math>|
  skewness  =|
  kurtosis  =|
  entropy    =|
  mgf        =|
  char      =|
}}
The '''shifted Gompertz distribution''' is the distribution of the largest of two independent [[random variable]]s one of which has an [[exponential distribution]] with parameter b and the other has a [[Gumbel distribution]] with parameters <math>\eta</math> and b. In its original formulation the distribution was expressed referring to the Gompertz distribution instead of the Gumbel distribution but, since the Gompertz distribution is a reverted Gumbel distribution ([[truncated distribution|truncated]] at zero), the labelling can be considered as accurate. It has been used as a model of [[Diffusion of innovations|adoption of innovations]]. It was proposed by Bemmaor (1994).  


==Statement==
== Specification ==
===Probability density function===


When a vector space over a [[Field (mathematics)|field]] ''F'' has a finite generating set, then one may extract from it a [[basis (vector space)|basis]] consisting of a finite number ''n'' of vectors, and the space is therefore isomorphic to ''F<sup>n</sup>''. The corresponding statement with the ''F'' generalized to a [[principal ideal domain]] ''R'' is no longer true, as a [[finitely generated module]] over ''R'' need not have any basis. However such a module is still isomorphic to a quotient of some module ''R<sup>n</sup>'' with ''n'' finite (to see this it suffices to construct the morphism that sends the elements of the canonical basis ''R<sup>n</sup>'' to the generators of the module, and take the quotient by its [[kernel (algebra)|kernel]].) By changing the choice of generating set, one can in fact describe the module as the quotient of some ''R<sup>n</sup>'' by a particularly simple submodule, and this is the structure theorem.
The [[probability density function]] of the shifted Gompertz distribution is:


The structure theorem for [[finitely generated module]]s over a [[principal ideal domain]] usually appears in the following two forms.
:<math> f(x;b,\eta) = b e^{-bx} e^{-\eta e^{-bx}}\left[1 + \eta\left(1 - e^{-bx}\right)\right] \text{ for }x \geq 0. \,</math>


===Invariant factor decomposition===
For every finitely generated module {{math|''M''}} over a principal ideal domain {{math|''R''}}, there is a unique decreasing sequence of proper ideals <math>(d_1)\supseteq(d_2)\supseteq\cdots\supseteq(d_n)</math> such that {{math|''M''}} isomorphic to the sum of cyclic modules:
:<math>M\cong\bigoplus_i R/(d_i) = R/(d_1)\oplus R/(d_2)\oplus\cdots\oplus R/(d_n).</math>
The generators <math>d_i</math> of the ideals are unique up to multiplication by a [[unit (ring theory)|unit]], and are called [[invariant factor]]s of ''M''. Since the ideals should be proper, these factors must not themselves be invertible (this avoids trivial factors in the sum), and the inclusion of the ideals means one has divisibility <math>d_1\mid d_2\mid\cdots\mid d_n</math>. The free part is visible in the part of the decomposition corresponding to  factors <math>d_i = 0</math>. Such factors, if any, occur at the end of the sequence.


While the direct sum is uniquely determined by {{math|''M''}}, the isomorphism giving the decomposition itself is ''not unique'' in general. For instance if {{math|''R''}} is actually a field, then all occurring ideals must be zero, and one obtains the decomposition of a finite dimensional vector space into a direct sum of one-dimensional subspaces; the number of such factors is fixed, namely the dimension of the space, but there is in a lot of freedom for choosing the subspaces themselves (if {{math|dim ''M'' &gt; 1}}).
where <math>b > 0</math> is the [[scale parameter]] and <math>\eta > 0</math> is the [[shape parameter]] of the shifted Gompertz distribution.


The nonzero <math>d_i</math> elements, together with the number of <math>d_i</math> which are zero, form a [[complete set of invariants]] for the module. Explicitly, this means that any two modules sharing the same set of invariants are necessarily isomorphic.
===Cumulative distribution function===


Some prefer to write the free part of ''M'' separately:
The [[cumulative distribution function]] of the shifted Gompertz distribution is:
:<math>R^f \oplus \bigoplus_i R/(d_i)  = R^f \oplus R/(d_1)\oplus R/(d_2)\oplus\cdots\oplus R/(d_{n-f})</math>
where the visible <math>d_i</math> are nonzero, and ''f'' is the number of <math>d_i</math>'s in the original sequence which are 0.


===Primary decomposition===
:<math> F(x;b,\eta) = \left(1 - e^{-bx}\right)e^{-\eta e^{-bx}} \text{ for }x \geq 0. \,</math>
:Every [[finitely generated module]] ''M'' over a [[principal ideal domain]] ''R'' is isomorphic to one of the form
::<math>\bigoplus_i R/(q_i)</math>
:where <math>(q_i) \neq R</math> and the <math>(q_i)</math> are [[primary ideal]]s. The <math>q_i</math> are unique (up to multiplication by units).


The elements <math>q_i</math> are called the ''elementary divisors'' of ''M''. In a PID, nonzero primary ideals are powers of primes, and so <math>(q_i)=(p_i^{r_i}) = (p_i)^{r_i}</math>. When <math>q_i=0</math>, the resulting indecomposable module is <math>R</math> itself, and this is inside the part of ''M'' that is a free module.


The summands <math>R/(q_i)</math> are [[indecomposable module|indecomposable]], so the primary decomposition is a decomposition into indecomposable modules, and thus every finitely generated module over a PID is a [[indecomposable module|completely decomposable module]]. Since PID's are Noetherian rings, this can be seen as a manifestation of the [[Lasker-Noether theorem]].
== Properties ==
The shifted Gompertz distribution is right-skewed for all values of <math>\eta</math>. It is more flexible than the [[Gumbel distribution]].  


As before, it is possible to write the free part (where <math>q_i=0</math>) separately and express ''M'' as:
===Shapes===
:<math>R^f \oplus(\bigoplus_i R/(q_i))</math>
The shifted Gompertz density function can take on different shapes depending on the values of the shape parameter <math>\eta</math>:
where the visible <math>q_i </math> are nonzero.
* <math>0 < \eta \leq 0.5\,</math> the probability density function has its mode at 0.
* <math>\eta > 0.5\,</math> the probability density function has its mode at
::<math>\text{mode}=-\frac{\ln(z^\star)}{b}\, \qquad 0 < z^\star < 1</math>  
:where <math>z^\star\,</math> is the smallest root of
::<math>\eta^2z^2 - \eta(3 + \eta)z + \eta + 1 = 0\,,</math>
:which is
::<math>z^\star = [3 + \eta - (\eta^2 + 2\eta + 5)^{1/2}]/(2\eta).</math>


==Proofs==
== Related distributions ==
One proof proceeds as follows:
If <math>\eta</math> varies according to a [[gamma distribution]] with shape parameter <math>\alpha</math> and scale parameter <math>\beta</math> (mean = <math>\alpha\beta</math>), the distribution of <math>x</math> is Gamma/Shifted Gompertz (G/SG). When <math>\alpha</math> is equal to one, the G/SG reduces to the [[Bass model]].
* Every [[finitely generated module]] over a PID is also [[finitely presented module|finitely presented]] because a PID is [[noetherian ring|Noetherian]], an even stronger condition than [[coherent ring|coherence]].
* Take a presentation, which is a map <math>R^r \to R^g</math> (relations to generators), and put it in [[Smith normal form]].
This yields the invariant factor decomposition, and the diagonal entries of Smith normal form are the invariant factors.


Another outline of a proof:
== See also ==
* Denote by ''tM'' the [[torsion submodule]] of M. Then ''M''/''tM'' is a finitely generated [[torsion-free module|torsion free]] module, and such a module over a commutative PID is a [[free module]] of finite rank, so it is isomorphic to <math>R^n</math> for a positive integer ''n''. This free module can be embedded as a submodule ''F'' of ''M'', such that the embedding splits (is a right inverse of) the projection map; it suffices to lift each of the generators of ''F'' into ''M''. As a consequence <math>M= tM\oplus F</math>.
*[[Gumbel distribution]]
* For a prime ''p'' in ''R'' we can then speak of <math>N_p= \{m\in tM\mid \exists i,  mp^i=0\}</math> for each prime ''p''.  This is a submodule of ''tM'', and it turns out that each ''N''<sub>''p''</sub> is a direct sum of cyclic modules, and that ''tM'' is a direct sum of ''N''<sub>''p''</sub> for a finite number of distinct primes ''p''.
*[[Generalized extreme value distribution]]
* Putting the previous two steps together, ''M'' is decomposed into cyclic modules of the indicated types.
*[[Mixture model]]
*[[Bass model]]
*[[Gompertz distribution]]


<!-- (commented out because it is a bit misleading and contains errors) * A finitely generated module is [[projection (mathematics)|projective]] if and only if it is [[localization of a module|locally]] [[free module|free]].
== References ==
* PIDs are [[Dedekind domains]], i.e., they are [[Noetherian ring|Noetherian]] and their [[Localization of a ring|localizations]] are [[discrete valuation ring]]s (DVRs).
{{No footnotes|date=April 2012}}
* Torsion free modules over DVRs are free. Hence, torsion free modules over PIDs are projective.
*{{Cite book | surname=Bemmaor | given=Albert C. | year= 1994 |pages=201–223| chapter=Modeling the Diffusion of New Durable Goods: Word-of-Mouth Effect Versus Consumer Heterogeneity | editor=G. Laurent, G.L. Lilien & B. Pras | title=Research Traditions in Marketing | publisher=Kluwer Academic Publishers | place=Boston| ISBN=0-7923-9388-0}}
* ''M/tM'' is torsion free, hence projective. Thus, ''M'' can be written as a direct sum of its torsion part and a projective part (in fact a free part), though not uniquely.
*{{Cite book| surname1=Chandrasekaran| given1=Deepa | surname2=Tellis| given2=Gerard J. |year= 2007 |volume=3|  chapter=A Critical Review of Marketing Research on Diffusion of New Products | editor=Naresh K. Malhotra  | title=Review of Marketing Research | publisher=M.E. Sharpe | place=Armonk | pages = 39–80 | ISBN = 978-0-7656-1306-6}}
*:That is, there is always a [[short exact sequence]] <math>0 \to tM \to M \to M/tM \to 0,</math> as the torsion part of a module is a submodule. By projectivity of <math>M/tM,</math> this has a splitting (a map <math>M/tM \to M</math> such that <math>M/tM \to M \to M/tM</math> is the identity).
*{{Cite journal
* If ''M'' is projective, so is a direct summand of a free module ''F = M + N''. One proves that ''N'' is locally 0, and hence is 0. Therefore, ''M'' is free.
  | last1 = Dover
* If ''M'' is torsion, it is the quotient of a free module. Using the ideas of the previous part, one proves it is a quotient by a free submodule, which must have rank equal to the original module. That is, torsion modules are finitely presented. Now use [[Smith normal form]].-->
  | first1 = Yaniv
  | title = Network Traces on Penetration: Uncovering Degree Distribution From Adoption Data 
  | first2 = Jacob |last2=Goldenberg
  | first3 = Daniel |last3=Shapira
  | journal = Marketing Science|doi=10.1287/mksc.1120.0711 |year=2012 }}
*{{Cite journal
  | last1 = Jimenez
  | first1 = Fernando
  | title = A Note on the Moments and Computer Generation of the Shifted Gompertz Distribution 
  | first2 = Pedro |last2=Jodra
  | journal = Communications in Statistics - Theory and Methods
  | volume = 38  | issue = 1
  | pages = 78–89
  | year = 2009
  | doi=10.1080/03610920802155502}}
*{{Cite journal
  | last1 = Van den Bulte
  | first1 = Christophe
  | title = Social Contagion and Income Heterogeneity in New Product Diffusion: A Meta-Analytic Test
  | first2 = Stefan |last2=Stremersch
  | journal = Marketing Science
  | volume = 23  | issue = 4
  | pages = 530–544
  | year = 2004
  | doi = 10.1287/mksc.1040.0054}}


==Corollaries==
{{ProbDistributions|continuous-semi-infinite}}
This includes the classification of [[finite-dimensional vector space]]s as a special case, where <math>R = K</math>. Since fields have no non-trivial ideals, every finitely generated vector space is free.


Taking <math>R=\mathbb{Z}</math> yields the [[fundamental theorem of finitely generated abelian groups]].
[[Category:Continuous distributions]]
 
Let ''T'' be a linear operator on a  [[finite-dimensional vector space]] ''V'' over ''K''. Taking <math>R=K[T]</math>, the algebra of polynomials with coefficients in ''K'' evaluated at ''T'', yields structure information about ''T''. ''V'' can be viewed as a finitely generated module over <math>K[T]</math>. The last invariant factor is the [[Minimal polynomial (field theory)|minimal polynomial]], and the product of invariant factors is the [[characteristic polynomial]]. Combined with a standard matrix form for <math>K[T]/p(T)</math>, this yields various [[canonical form]]s:
* [[invariant factors]] + [[companion matrix]] yields [[Frobenius normal form]] (aka, [[rational canonical form]])
* [[primary decomposition]] + [[companion matrix]] yields [[primary rational canonical form]]
* [[primary decomposition]] + [[Jordan block]]s yields [[Jordan canonical form]] (this latter only holds over an [[algebraically closed field]])
 
==Uniqueness==
While the invariants (rank, invariant factors, and elementary divisors) are unique, the isomorphism between ''M'' and its [[canonical form]] is not unique, and does not even preserve the [[direct sum of modules|direct sum]] decomposition. This follows because there are non-trivial automorphisms of these modules which do not preserve the summands.
 
However, one has a canonical torsion submodule ''T'', and similar canonical submodules corresponding to each (distinct) invariant factor, which yield a canonical sequence:
:<math>0 < \cdots < T < M.</math>
Compare [[composition series]] in [[Jordan–Hölder theorem]].
 
For instance, if <math>M \approx \mathbf{Z} \oplus \mathbf{Z}/2</math>, and <math>(1,0), (0,1)</math> is one basis, then
<math>(1,1), (0,1)</math> is another basis, and the change of basis matrix <math>\begin{bmatrix}1 & 1 \\0 & 1\end{bmatrix}</math> does not preserve the summand <math>\mathbf{Z}</math>. However, it does preserve the <math>\mathbf{Z}/2</math> summand, as this is the torsion submodule (equivalently here, the 2-torsion elements).
 
==Generalizations==
===Groups===
The [[Jordan–Hölder theorem]] is a more general result for finite groups (or modules over an arbitrary ring). In this generality, one obtains a [[composition series]], rather than a [[direct sum of modules|direct sum]].
 
The [[Krull–Schmidt theorem]] and related results give conditions under which a module has something like a primary decomposition, a decomposition as a direct sum of [[indecomposable module]]s in which the summands are unique up to order.
 
===Primary decomposition===
The primary decomposition generalizes to finitely generated modules over commutative [[Noetherian ring]]s, and this result is called the [[Lasker–Noether theorem]].
 
===Indecomposable modules===
By contrast, unique decomposition into ''indecomposable'' submodules does not generalize as far, and the failure is measured by the [[ideal class group]], which vanishes for PIDs.
 
For rings that are not principal ideal domains, unique decomposition need not even hold for modules over a ring generated by two elements. For the ring R&nbsp;=&nbsp;Z[√−5], both the module R and its submodule M generated by 2 and 1&nbsp;+&nbsp;√−5 are indecomposable. While R is not isomorphic to M, R&nbsp;⊕&nbsp;R is isomorphic to M&nbsp;⊕&nbsp;M; thus the images of the M summands give indecomposable submodules L<sub>1</sub>,&nbsp;L<sub>2</sub>&nbsp;<&nbsp;R&nbsp;⊕&nbsp;R which give a different decomposition of R&nbsp;⊕&nbsp;R. The failure of uniquely factorizing R&nbsp;⊕&nbsp;R into a direct sum of indecomposable modules is directly related (via the ideal class group) to the failure of the unique factorization of elements of R into irreducible elements of&nbsp;R.
 
===Non-finitely generated modules===
Similarly for modules that are not finitely generated, one cannot expect such a nice decomposition: even the number of factors may vary.  There are '''Z'''-submodules of '''Q'''<sup>4</sup> which are simultaneously direct sums of two indecomposable modules and direct sums of three indecomposable modules, showing the analogue of the primary decomposition cannot hold for infinitely generated modules, even over the integers, '''Z'''.
 
Another issue that arises with non-finitely generated modules is that there are torsion-free modules which are not free. For instance, consider the ring '''Z''' of integers. Then '''Q''' is a torsion-free '''Z'''-module which is not free. Another classical example of such a module is the [[Baer–Specker group]], the group of all sequences of integers under termwise addition. In general, the question of which infinitely generated torsion-free abelian groups are free depends on which [[large cardinal]]s exist. A consequence is that any structure theorem for infinitely generated modules depends on a choice of set theory axioms and may be invalid under a different choice.
 
==References==
{{reflist}}
{{refbegin}}
*{{Citation | last1=Dummit | first1=David S. | last2=Foote | first2=Richard M. | title=Abstract algebra | publisher=Wiley | location=New York | edition=3rd | isbn=978-0-471-43334-7 |mr=2286236 | year=2004}}
*{{Citation | last=Hungerford | first1=Thomas W. | author1-link=Thomas W. Hungerford | title=Algebra | publisher=Springer | location=New York | isbn=978-0-387-90518-1 | year=1980 | pages=218–226, Section IV.6: Modules over a Principal Ideal Domain }}
*{{Citation  |author=Jacobson, Nathan  |author1-link=Nathan Jacobson|title=Basic algebra. I  |edition=2  |publisher=W. H. Freeman and Company  |place=New York  |date=1985  |pages=xviii+499  |isbn=0-7167-1480-9  |mr=780184}}
*{{Citation | last1=Lam | first1=T. Y. | title=Lectures on modules and rings | publisher=Springer-Verlag | series=Graduate Texts in Mathematics No. 189 | isbn=978-0-387-98428-5 | year=1999}}
{{refend}}
 
{{DEFAULTSORT:Structure Theorem For Finitely Generated Modules Over A Principal Ideal Domain}}
[[Category:Theorems in abstract algebra]]
[[Category:Module theory]]
 
[[de:Hauptidealring#Moduln über Hauptidealringen]]

Revision as of 23:01, 15 August 2014

Template:Probability distribution The shifted Gompertz distribution is the distribution of the largest of two independent random variables one of which has an exponential distribution with parameter b and the other has a Gumbel distribution with parameters and b. In its original formulation the distribution was expressed referring to the Gompertz distribution instead of the Gumbel distribution but, since the Gompertz distribution is a reverted Gumbel distribution (truncated at zero), the labelling can be considered as accurate. It has been used as a model of adoption of innovations. It was proposed by Bemmaor (1994).

Specification

Probability density function

The probability density function of the shifted Gompertz distribution is:


where is the scale parameter and is the shape parameter of the shifted Gompertz distribution.

Cumulative distribution function

The cumulative distribution function of the shifted Gompertz distribution is:


Properties

The shifted Gompertz distribution is right-skewed for all values of . It is more flexible than the Gumbel distribution.

Shapes

The shifted Gompertz density function can take on different shapes depending on the values of the shape parameter :

where is the smallest root of
which is

Related distributions

If varies according to a gamma distribution with shape parameter and scale parameter (mean = ), the distribution of is Gamma/Shifted Gompertz (G/SG). When is equal to one, the G/SG reduces to the Bass model.

See also

References

Template:No footnotes

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    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  • One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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