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This page describes the mathematical concept of a 'ring'. You might also be interested in [web ring]? or [jewelry ring]?. |
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The original contents of this page have been moved to Mathematical ring so that all kinds of rings such as [web ring]? or [jewelry ring]? can be discussed here. |
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A Ring is a commutative Group under an operation +, together with a second operation * s.t. a*(b*c) = (a*b)*c a*(b+c) = (a*b)+(a*c), (a+b)*c = (a*c)+(b*c) Very often the definition of a ring is taken to require a multiplicative identity, or unity, denoted 1. Nearly all important rings actually satisfy this. It has the disadvantage, however, of making ring ideals not subrings, as compared with their group-analog, the normal subgroups. A ring is commutative if its multiplication is commutative. Some important concepts: subrings and ideals, Modules A ring where no two non-zero elements multiply to give zero is called an [integral domain]?. In such rings, multiplicative cancellation is possible. Of particular interest are fields, integral domains where every non-zero element has a muliplicative inverse. Somebody please rename this to mathematical ring! |
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