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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 all x, y E R.
Transcribed Image Text: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 all x, y E R.
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