(a) Let G be an (additive) abelian group. Define an operation of multiplication in G by ab...
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(a) Let G be an (additive) abelian group. Define an operation of multiplication in G by ab = 0 (for all a,b ϵ G). Then G is a ring.
(b) Let S be the set of all subsets of some fixed set U. For A,B ϵ S, define A + B = (A - B) U (B - A) and AB = A ∩ B. Then S is a ring. Is S commutative? Does it have an identity?
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a To show that G is a ring we need to show that it satisfies the ring axioms 1 G is an abelian group ...View the full answer
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Related Book For 
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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