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).)

Given: V=Vx3-y2⊂A2 ϕ:A1→V by ϕt=t2,t3 To do: Show that ϕ is a bijection but not an isomorphism.…

Answered: Let V = V(r - y) C A. Consider the…

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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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).)