(a) Give an example of a nonzero homomorphism : R S of rings with identity...
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(a) Give an example of a nonzero homomorphism ∫ : R → S of rings with identity such that ∫(1R) ≠ 1s.
(b) If ∫: R → S is an epimorphism of rings with identity, then ∫(1R) = 1s.
(c) If ∫: R → S is a homomorphism of rings with identity and u is a unit in R such that ∫(u) is a unit in S, then ∫(1R) = 1s and ∫(u-1) = f(u)-1•
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a Let R be the ring with identity 0 1 and addition and multiplication defined as follows 0 0 0 0 1 1 ...View the full answer
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Related Book For 
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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