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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![2. Let V = V(r-y²) C A?. Consider the morphism o: A'V given by 6(t) = (t2,P).
(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).)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9cdea79-1c3e-46c9-9c06-26ef863fac64%2F6af21ffc-08d5-4f25-b18e-c4b60ef4e0a7%2F0mj1znm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let V = V(r-y²) C A?. Consider the morphism o: A'V given by 6(t) = (t2,P).
(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).)
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