An element a of a ring R is nilpotent if a n = 0 for some n

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An element a of a ring R is nilpotent if aⁿ = 0 for some n ∈ Z⁺. Show that if a and b are nilpotent elements of a commutative ring, then a + b is also nilpotent.

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A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

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Question Posted: Jan 05, 2023 05:27 AM

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An element a of a ring R is nilpotent if a n = 0 for some n

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As explained in the answer to Exercise 41 the binomial expansion is valid in a com...View the full answer

A First Course In Abstract Algebra

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