Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideals, and modules over such rings....

In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center...

some subjects such as algebraic geometry, unital associative commutative algebra. Replacing the field of scalars by a commutative ring leads to the more...

In commutative algebra and algebraic geometry, localization is a formal way to introduce the "denominators" to a given ring or module. That is, it introduces...

a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Complementarily...

Equivalently, a noncommutative ring is a ring that is not a commutative ring. Noncommutative algebra is the part of ring theory devoted to study of properties...

necessarily commutative" for noncommutative rings. An algebra is unital or unitary if it has an identity element e with ex = x = xe for all x in the algebra. For...

In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist...

ring may be regarded as a free commutative algebra. For R a commutative ring, the free (associative, unital) algebra on n indeterminates {X1,...,Xn}...

involutive rings R and A, where R is commutative and A has the structure of an associative algebra over R. Involutive algebras generalize the idea of a number...