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A ring with a unit element in which every element is idempotent.

A quotient ring (also called a residue-class ring) is a ring that is the quotient of a ring A and one of its ideals a, denoted A/a. For example, when the ring A is Z (the ...

A ring defined on a singleton set {*}. The ring operations (multiplication and addition) are defined in the only possible way, *·*=*, (1) and *+*=*. (2) It follows that this ...

The ring of integers is the set of integers ..., -2, -1, 0, 1, 2, ..., which form a ring. This ring is commonly denoted Z (doublestruck Z), or sometimes I (doublestruck I). ...

Given a module M over a unit ring R, the set End_R(M) of its module endomorphisms is a ring with respect to the addition of maps, (f+g)(x)=f(x)+g(x), for all x in M, and the ...

Given a set X, let F be a nonempty set of subsets of X. Then F is a ring if, for every pair of sets in F, the intersection, union, and set difference is also in F. F is ...

A graded algebra over the integers Z. Cohomology of a space is a graded ring.

A ring in the mathematical sense is a set S together with two binary operators + and * (commonly interpreted as addition and multiplication, respectively) satisfying the ...

A unit in a ring is an element u such that there exists u^(-1) where u·u^(-1)=1.

A commutative unit ring having only finitely many maximal ideals.