In a commutative ring R with identity the following conditions are equivalent: (i) R has a unique

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In a commutative ring R with identity the following conditions are equivalent:

(i) R has a unique prime ideal;

(ii) every nonunit is nilpotent

(iii) R has a minimal prime ideal which contains all zero divisors, and all nonunits of Rare zero divisors.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 15, 2023 03:05 AM

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In a commutative ring R with identity the following conditions are equivalent: (i) R has a unique

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First we will show that i implies ii Suppose R has a unique prime ideal P If x R is not a unit then ...View the full answer

Algebra Graduate Texts In Mathematics 73

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