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There are two types of bordism groups: bordism groups, also called cobordism groups or cobordism rings, and there are singular bordism groups. The bordism groups give a ...

If G is a perfect group, then the group center of the quotient group G/Z(G), where Z(G) is the group center of G, is the trivial group.

For X a topological space, the presheaf F of Abelian groups (rings, ...) on X is defined such that 1. For every open subset U subset= X, an Abelian group (ring, ...) F(U), ...

The cokernel of a group homomorphism f:A-->B of Abelian groups (modules, or abstract vector spaces) is the quotient group (quotient module or quotient space, respectively) ...

A subring of a ring R is a subgroup of R that is closed under multiplication.

An associative ring, also called a Hecke ring, which has a technical definition in terms of commensurable subgroups.

A more common way to describe a Euclidean ring.

An extension ring R subset= S such that every element of S is integral over R.

Any linear system of point-groups on a curve with only ordinary singularities may be cut by adjoint curves.

The ring of integers of a number field K, denoted O_K, is the set of algebraic integers in K, which is a ring of dimension d over Z, where d is the extension degree of K over ...