Student Solutions Manual for Gallian's Contemporary Abstract Algebra, 9th
Student Solutions Manual for Gallian's Contemporary Abstract Algebra, 9th
9th Edition
ISBN: 9781305657977
Author: Gallian, Joseph
Publisher: Brooks Cole
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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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