) Let R be a commutative ring and f : R → S be a ring isomorphism. Then (i) check as to whether S is also commutataive or not (ii) what can you conclude about commutativity and isomorphisms

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 15E: Let I be an ideal in a ring R with unity. Prove that if I contains an element a that has a...
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(b) Let R be a commutative ring and f: R → S be a ring isomorphism. Then
(i) check as to whether S is also commutataive or not
(ii) what can you conclude about commutativity and isomorphisms
Transcribed Image Text:(b) Let R be a commutative ring and f: R → S be a ring isomorphism. Then (i) check as to whether S is also commutataive or not (ii) what can you conclude about commutativity and isomorphisms
Let R be a ring and S be a subring of R. Then prove that 0s = OR, where Os, OR are the zero
elements in S, R respectively
Transcribed Image Text:Let R be a ring and S be a subring of R. Then prove that 0s = OR, where Os, OR are the zero elements in S, R respectively
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