A note on the coefficient rings of polynomial rings |
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Authors: | J H Pathak |
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Affiliation: | 1. Department of Mathematics, University of Bombay, Vidyanagari, 400 098, Bombay
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Abstract: | LetA andB be two reduced commutative rings with finitely many minimal prime ideals. If the polynomial algebrasA[X 1 …X n ]=B[Y 1 …Y n ] whereX i ,Y iF are variables overA andB respectively, then there exists an injective ring homomorphism ϕ:A→B such thatB is finitely generated over ϕ(A). |
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Keywords: | Polynomial ring integral extension minimal primes |
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