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