Exercise 11.2. Let R be a ring. Show that for every nilpotent element a = R (i.e. an = 0 for some nЄ N), the polynomial 1 – ax Є R[x] is a unit in R[x].

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.1: Ideals And Quotient Rings
Problem 1E: Exercises Let I be a subset of ring R. Prove that I is an ideal of R if and only if I is nonempty...
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Exercise 11.2. Let R be a ring. Show that for every nilpotent element a = R (i.e. an = 0 for some
nЄ N), the polynomial 1 – ax Є R[x] is a unit in R[x].
Transcribed Image Text:Exercise 11.2. Let R be a ring. Show that for every nilpotent element a = R (i.e. an = 0 for some nЄ N), the polynomial 1 – ax Є R[x] is a unit in R[x].
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