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

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 4E: [Type here] Examples 5 and 6 of Section 5.1 showed that is a commutative ring with unity. In...

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