Ring theory

In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic p, an important class which includes finite fields.

An integer (from the Latin integer meaning "whole") is a number that can be written without a fractional component.

In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts.

In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.

In commutative algebra, an element b of a commutative ring B is said to be integral over A, a subring of B, if there are n ≥ 1 and such that That is to say, b is a root of a monic polynomial over A.

In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal is equal to its Krull dimension.

In mathematics, an invertible element or a unit in a (unital) ring R is any element u that has an inverse element in the multiplicative monoid of R, i.

In mathematics, the symmetric algebra S(V) (also denoted Sym(V)) on a vector space V over a field K is the free commutative unital associative algebra over K containing V.

In algebra, a torsion-free module is a module over a ring such that 0 is the only element annihilated by a regular element (non zero-divisor) of the ring.

A geometric algebra (GA) is a Clifford algebra of a vector space over the field of real numbers endowed with a quadratic form.

In abstract algebra, in particular in the theory of nondegenerate quadratic forms on vector spaces, the structures of finite-dimensional real and complex Clifford algebras have been completely classified.

In number theory, quadratic integers are a generalization of the integers to quadratic fields.

In algebra, a Hilbert ring or a Jacobson ring is a ring such that every prime ideal is an intersection of primitive ideals.