Let V = V(r - y) C A. Consider the morphism o: A' → V given by o(t) = (t,t). (a) Show that o is a bijection but not an isomorphism. (b) Show that V is not isomorphic to A'. (Note that this is not implied by (a).)
Let V = V(r - y) C A. Consider the morphism o: A' → V given by o(t) = (t,t). (a) Show that o is a bijection but not an isomorphism. (b) Show that V is not isomorphic to A'. (Note that this is not implied by (a).)
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.2: Complex Numbers And Quaternions
Problem 50E
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