commutative ring

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• Commutative ring — In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative. The study of commutative rings is called commutative algebra. Some specific kinds of commutative rings are given with …   Wikipedia

• Ring — /ring/, n. a male given name. * * * I Circular band of gold, silver, or other precious or decorative material usually worn on the finger, but sometimes on the toes, the ears, or the nose. The earliest examples were found in the tombs of ancient… …   Universalium

• Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …   Wikipedia

• Ring theory — In abstract algebra, ring theory is the study of rings algebraic structures in which addition and multiplication are defined and have similar properties to those familiar from the integers. Ring theory studies the structure of rings, their… …   Wikipedia

• Commutative algebra — This page deals with the area of study. For algebras which are commutative, see algebra (disambiguation). Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both… …   Wikipedia

• Commutative property — For other uses, see Commute (disambiguation). In mathematics an operation is commutative if changing the order of the operands does not change the end result. It is a fundamental property of many binary operations, and many mathematical proofs… …   Wikipedia

• ring — ring1 ringless, adj. ringlike, adj. /ring/, n., v., ringed, ringing. n. 1. a typically circular band of metal or other durable material, esp. one of gold or other precious metal, often set with gems, for wearing on the finger as an ornament, a… …   Universalium

• Ring homomorphism — In ring theory or abstract algebra, a ring homomorphism is a function between two rings which respects the operations of addition and multiplication. More precisely, if R and S are rings, then a ring homomorphism is a function f : R → S such that …   Wikipedia

• Ring of integers — In mathematics, the ring of integers is the set of integers making an algebraic structure Z with the operations of integer addition, negation, and multiplication. It is a commutative ring, and is the prototypical such by virtue of satisfying only …   Wikipedia

• Ring of mixed characteristic — In commutative algebra, a ring of mixed characteristic is a commutative ring R having characteristic zero and having an ideal I such that R / I has positive characteristic. Examples The integers Z have characteristic zero, but for any prime… …   Wikipedia

• commutative — adjective a) Such that the order in which the operands are taken does not affect their image under the operation. Addition on the real numbers is commutative because for any real numbers , . b) Having a commutative operation. Syn: abelian …   Wiktionary