Let : Z Z 2 be the canonical epimorphism. The induced map : Hom(Z 2
Question:
Let π : Z → Z2 be the canonical epimorphism. The induced map π̅: Hom(Z2,Z) - Hom(Z2,Z2) is the zero map. Since Hom(Z2,Z2) ≠ 0 (Exercise 1(b)), π̅ is not an epimorphism.
Data from exercise 1(b)
(b) Hom(Zm,Zn) ≅ Z(m,n).
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Based on exercise 1b we have that HomZ2 Z2 is isomorphic to Z22 which is isomorphic to Z2 Thi...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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