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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Prime ideals in polynomial rings over one-dimensional domains


Authors: William Heinzer and Sylvia Wiegand
Journal: Trans. Amer. Math. Soc. 347 (1995), 639-650
MSC: Primary 13B25; Secondary 13A15
MathSciNet review: 1242087
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Abstract: Let $ R$ be a one-dimensional integral domain with only finitely many maximal ideals and let $ x$ be an indeterminate over $ R$. We study the prime spectrum of the polynomial ring $ R[x]$ as a partially ordered set. In the case where $ R$ is countable we classify $ \operatorname{Spec} (R[x])$ in terms of splitting properties of the maximal ideals $ {\mathbf{m}}$ of $ R$ and the valuative dimension of $ {R_{\mathbf{m}}}_{}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1242087-5
PII: S 0002-9947(1995)1242087-5
Article copyright: © Copyright 1995 American Mathematical Society