Answered: (a) Let R be a commutative ring with M…

(a) Let R be a commutative ring with M being maximal ideal in R then R/M is a field. (b) If R is a commutative ring with a, be R then g.c.d (a, b) is unique.

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 3TFE

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Question

Prove or disprove the following:
(a) Let R be a commutative ring with M being maximal ideal in R then R/M is a field.
(b) If R is a commutative ring with a, bE R then g.c.d (a, b) is unique.
(a) In C the element 3+ 4i is an associate of the element -4+3i.

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