9th Edition

ISBN: 9781305657960

Author: Joseph Gallian

Publisher: Cengage Learning

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Chapter 13, Problem 15E

Let a belong to a ring R with unity and suppose that a n = 0 forsome positive integer n. (Such an element is called nilpotent.) Provethat 1 − a has a multiplicative inverse in R. [Hint: Consider ( 1 − a ) ( 1 + a + a 2 + ⋯ + a n − 1 ) .]

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Chapter 13, Problem 14E

Chapter 13, Problem 16E

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Chapter 13 Solutions

Contemporary Abstract Algebra

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Let a belong to a ring R with unity and suppose that a n = 0 forsome positive integer n . (Such an element is called nilpotent.) Provethat 1 − a has a multiplicative inverse in R . [ Hint: Consider ( 1 − a ) ( 1 + a + a 2 + ⋯ + a n − 1 ) .]

Solution Summary: The author explains that (1-a) has a multiplicative inverse in R.

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Chapter 13 Solutions