The following are equivalent (a) R is prime (b) a, b R and aRb 0 imply a 0 or b 0 (c) The right annihilator of every nonzero right ideal of R is 0 (d) The left annihilator of every nonzero left ideal of R is 0 ...

To understand the equivalence of the statements a b c and d lets first define some terms A ring R is a set equipped with two binary operations usually ...

The following are equivalent: (a) R is prime; (b) a, b R and aRb = 0

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The following are equivalent:

(a) R is prime;

(b) a, b ϵ R and aRb = 0 imply a = 0 or b = 0;

(d) The left annihilator of every nonzero left ideal of R is 0.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Aug 03, 2023 08:21 AM

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The following are equivalent: (a) R is prime; (b) a, b R and aRb = 0

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Algebra Graduate Texts In Mathematics 73

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