Answered: (b) Show that if : R→ S is only assumed…

(b) Show that if : R→ S is only assumed to be a ring homomorphism, then it is possible to have a zero divisor z R for which o(r) is not a zero divisor in S.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.1: Definition Of A Ring

Problem 24E: Prove that if a is a unit in a ring R with unity, then a is not a zero divisor.

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(b)
Show that if : R S is only assumed to be a ring homomorphism, then it is
possible to have a zero divisor x R for which o(r) is not a zero divisor in S.

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