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.
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.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.1: Polynomials Over A Ring
Problem 18E: 18. Let be a commutative ring with unity, and let be the principal ideal in . Prove that is...
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