An element of a ring is nilpotent if a n = 0 for some n. Prove that

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An element of a ring is nilpotent if aⁿ = 0 for some n. Prove that in a commutative ring a + b is nilpotent if a and b are. Show that this result may be false if R is not commutative.

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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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An element of a ring is nilpotent if a n = 0 for some n. Prove that

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Let a b be nilpotent elements in a commutative ring R This means that there exist positive integers ...View the full answer

Algebra Graduate Texts In Mathematics 73

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