commutative-associative ring

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• 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 — /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 — ring1 [riŋ] vi. rang or Now Chiefly Dial. rung, rung, ringing [ME ringen < OE hringan < IE echoic base * ker > RAVEN1, CREAK, L corvus, crow] 1. to give forth a clear, resonant sound when struck or otherwise caused to vibrate, as a bell …   English World dictionary

• 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

• 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

• 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

• Associative algebra — In mathematics, an associative algebra is a vector space (or more generally, a module) which also allows the multiplication of vectors in a distributive and associative manner. They are thus special algebras. Definition An associative algebra A… …   Wikipedia

• Associative property — This article is about associativity in mathematics. For associativity in the central processor unit memory cache, see CPU cache. For associativity in programming languages, see operator associativity. In mathematics, associativity is a property… …   Wikipedia

• ring — I [[t]rɪŋ[/t]] n. 1) jew a typically circular band of durable material, as gold, worn on the finger as an ornament, a token of betrothal or marriage, etc 2) anything having the form of such a band: a smoke ring[/ex] 3) a circular line or mark:… …   From formal English to slang

• ring — I. noun Etymology: Middle English, from Old English hring; akin to Old High German hring ring, Old Church Slavic krǫgŭ circle Date: before 12th century 1. a circular band for holding, connecting, hanging, pulling, packing, or sealing < a key ring …   New Collegiate Dictionary

• Matrix ring — In abstract algebra, a matrix ring is any collection of matrices forming a ring under matrix addition and matrix multiplication. The set of n×n matrices with entries from another ring is a matrix ring, as well as some subsets of infinite matrices …   Wikipedia