Kailashben 1. Let R be a ring, and let ICR be an ideal. Prove that R/I is commutative if and only if xy –yxE I for allx, y E R.

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Answered: Let R be a ring, and let ICR be an…

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 4E: Exercises If and are two ideals of the ring , prove that is an ideal of .

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Let R be a ring, and let ICR be an ideal. Prove that R/I is commutative if and only if xy - yx € I for all x, y E R.