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Commutative Ring

  • Definition: A ring R is a set with two laws of composition + and x, called addition and multiplication, that satisfy these axioms: a) With the law of composition +, R is an abelian group; its identity is denoted by 0. b) Multiplication is commutative and associative, and has an identity denoted by . c) Distributive law: For all a, b, and c in R, (a+b)c=ac+ab.

    Source: Algebra, second edition by Michael Artin

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