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...

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

Extracted text: 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.

Jun 04, 2022

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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...

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