Let f:R→s be a ring homomorphism. (i) Prove that if K is a subring of then f(K) is a subring of s. (ii) Prove that f is one to one if and only if Kerf={0}: R
Let f:R→s be a ring homomorphism. (i) Prove that if K is a subring of then f(K) is a subring of s. (ii) Prove that f is one to one if and only if Kerf={0}: 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 7E: Exercises
Let be an ideal of a ring , and let be a subring of . Prove that is an ideal of
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