I'm reading a proof concerning a factor ring R/I. And I have come across the following sequence of steps: 1. Since R/I is commutative then (r+I)(s+I)=(s+I)(r+I) (I is an ideal of R) 2. This implies that rs+I=sr+I 3. This implies that rs-sr is an element of I I don't see how step 2 implies step 3

I'm reading a proof concerning a factor ring R/I. And I have come across the following sequence of steps: 1. Since R/I is commutative then (r+I)(s+I)=(s+I)(r+I) (I is an ideal of R) 2. This implies that rs+I=sr+I 3. This implies that rs-sr is an element of I I don't see how step 2 implies step 3

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 11E: 11. a. Give an example of a ring of characteristic 4, and elements in such that b. Give an...

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I'm reading a proof concerning a factor ring R/I. And I have come across the following sequence of steps:

1. Since R/I is commutative then (r+I)(s+I)=(s+I)(r+I) (I is an ideal of R)

2. This implies that rs+I=sr+I

3. This implies that rs-sr is an element of I

I don't see how step 2 implies step 3

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