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| In mathematics, a '''binomial ring''' is a [[ring (mathematics)|ring]] whose additive [[group (mathematics)|group]] is [[torsion (algebra)|torsion-free]] that contains all [[binomial coefficient]]s
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| :<math>\binom{x}{n} = \frac{x(x-1)\cdots(x-n+1)}{n!}</math> | |
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| for ''x'' in the ring and ''n'' a positive integer. Binomial rings were introduced by {{harvtxt|Hall|1969}}.
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| {{harvtxt|Elliott|2006}} showed that binomial rings are essentially the same as [[lambda ring|λ-rings]] such that all [[Adams operation]]s are the identity.
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| ==References==
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| *{{Citation | last1=Elliott | first1=Jesse | title=Binomial rings, integer-valued polynomials, and λ-rings | doi=10.1016/j.jpaa.2005.09.003 | mr=2244389 | year=2006 | journal=Journal of Pure and Applied Algebra | issn=0022-4049 | volume=207 | issue=1 | pages=165–185}}
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| *{{Citation | last1=Hall | first1=Philip | author1-link=Philip Hall | title=The Edmonton notes on nilpotent groups. Notes of lectures given at the Canadian Mathematical Congress Summer Seminar (University of Alberta, 12–30 august 1957) | origyear=1957 | url=http://books.google.com/books?id=eeruAAAAMAAJ | publisher=Mathematics Department, Queen Mary College, London | series=Queen Mary College Mathematics Notes | isbn=978-0-902480-06-3 | mr=0283083 | year=1969}}
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| *{{citation|mr=2649360
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| |last=Yau|first= Donald
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| |title=Lambda-rings|publisher= World Scientific Publishing Co. Pte. Ltd.|place= Hackensack, NJ|year= 2010 |isbn= 978-981-4299-09-1 |url=http://books.google.com/books?id=d7vKnjxyvxQC}}
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| [[Category:Ring theory]]
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Latest revision as of 20:24, 17 August 2014
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