Answered: Let R = Q[V2] and S = Q[V3]. Show that… | bartleby

Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 5E

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Let R = Q[V2] and S = Q[V3]. Show that the only ring homomorphism
from R to S is the trivial one. In particular, conclude that R and S
are not isomorphic rings. In other words, assume f : R → S is a ring
homomorphism. Show that f (r) = 0 for allr E R.

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