Theorem 1 [Universal Property] Let : F→ R be a ring homo-morphism, where R is a commutative ring with unity. Let b₁,..., bn besome arbitrary elements of R. Then there exists a unique ring homo-morphism &: F[x1, ..., xn] → R such that (1) vo€ = ¢ (2) ¥(x₁) = bivoe:for all i = 1,..., n.

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Answered: : F[x₁,...,xn] → R such that (1) € =…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.2: Ring Homomorphisms

Problem 11E: 11. Show that defined by is not a homomorphism.

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: F[x₁,...,xn] → R such that (1) € = (2) √(x₁) = bi