Let f.R→s be a ring homomorphism.(i) Prove that if K is a subring of R then fn is a subring ofr(K)is one to one if and only if Kerf={0}·(i) Prove that f is one to one if and only if Kerf= {0}-%D

Given, if f:R→S be a ring homomorphism. (i) To prove that if K is a subring of R then f(K) is a…

Answered: R→s be a ring homomorphism. ve that if…

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R→s be a ring homomorphism. ve that if K is a subring of then R f(K) is a subring of S ve that c is ono to opo if pnd

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let f.R→s be a ring homomorphism.
(i) Prove that if K is a subring of R then fn is a subring of
r(K)
is one to one if and only if Kerf={0}·
(i) Prove that f is one to one if and only if Kerf= {0}-
%D

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