# Pseudo-ring

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In mathematics, and more specifically in abstract algebra, a **pseudo-ring** is one of the following variants of a ring:

- A rng, i.e., a structure satisfying all the axioms of a ring except for the existence of a multiplicative identity.
^{[1]} - A set
*R*with two binary operations + and · such that (*R*,+) is an abelian group with identity 0, and and for all*a*,*b*,*c*in*R*.^{[2]} - An abelian group (
*A*,+) equipped with a subgroup*B*and a multiplication*B*×*A*→*A*making*B*a ring and*A*a*B*-module.^{[3]}

No two of these definitions are equivalent, so it is best to avoid the term "pseudo-ring" or to clarify which meaning is intended.

## See also

- Semiring – an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse