Answered: 9. Suppose that (R,+,.) be a…

9. Suppose that (R,+,.) be a commutative ring with identity and x E rad R, then (a) (x) = R (b) 1 — х€R* (c) (1+ x) # R (d) No Choice

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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Question

9. Suppose that (R,+,.) be a commutative ring with identity and x E rad R, then
(a) (x) = R
(Φ) 1-xER
(c) (1+ x) + R
(d) No Choice

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