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Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.1: Polynomials Over A Ring

Problem 15E: 15. Prove that if is an ideal in a commutative ring with unity, then is an ideal in .

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Suppose R is a commutative ring with 1R 0R.
Show that if f (x) = ao + a1x + a2x" + + ana" is a unit in Rc), then ao is a
unit in R and each of a1, a2, , an is nilpotent.
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