Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Theorem 1 [Universal Property] Let : F→ R be a ring homo- morphism, where R is a commutative ring with unity. Let b₁,..., bn be some arbitrary elements of R. Then there exists a unique ring homo- morphism &: F[x1, ..., xn] → R such that (1) vo€ = ¢ (2) ¥(x₁) = bi voe: for all i = 1,..., n.
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Transcribed Image Text:Theorem 1 [Universal Property] Let : F→ R be a ring homo- morphism, where R is a commutative ring with unity. Let b₁,..., bn be some arbitrary elements of R. Then there exists a unique ring homo- morphism &: F[x1, ..., xn] → R such that (1) vo€ = ¢ (2) ¥(x₁) = bi voe: for all i = 1,..., n.
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