Please ans this with in 15 to 30 mins to get a thumbs up! Please show neat and clean work . 6. (a) (Suppose : R S is a ring isomorphism. Show that if x is a zero divisor in R, theno(a) is a zero divisor in S.(b)*Show that if : R S is only assumed to be a ring homomorphism, then it ispossible to have a zero divisor z R for which o(r) is not a zero divisor in S.

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(a) Suppose : R→ S is a ring isomorphism. Show that if z is a zero divisor in R, then (2) is a zero divisor in S. (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(z) is not a zero divisor in S.

(a) Suppose : R→ S is a ring isomorphism. Show that if z is a zero divisor in R, then (2) is a zero divisor in S. (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(z) is not a zero divisor in S.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 19E: 19. a. Show that is isomorphic to , where the group operation in each of , and is addition. ...

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Please ans this with in 15 to 30 mins to get a thumbs up! Please show neat and clean work .

6. (a) (
Suppose : R S is a ring isomorphism. Show that if x is a zero divisor in R, then
o(a) is a zero divisor in S.
(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.

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