If ø is a ring homomorphism from R to S. ThenProve that (ker o) is an ideal of S.i.Prove that o(Imø) is an ideal of R.Explain (i) and (ii) also with an example.ii.iii.

Given φ is a ring homomorphism from R to S. To prove: φkerφ is an ideal of S. Given, φ: R→S is a…

Answered: If ø is a ring homomorphism from R to…

If ø is a ring homomorphism from R to S. Then i. ii. Prove that (kero) is an ideal of S. Prove that o'Imø) is an ideal of R.

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 8E: Exercises If and are two ideals of the ring , prove that the set is an ideal of that contains...

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If ø is a ring homomorphism from R to S. Then
Prove that (ker o) is an ideal of S.
i.
Prove that o(Imø) is an ideal of R.
Explain (i) and (ii) also with an example.
ii.
iii.

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