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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Prime ideals in two-dimensional polynomial rings


Authors: William Heinzer and Sylvia Wiegand
Journal: Proc. Amer. Math. Soc. 107 (1989), 577-586
MSC: Primary 13B25; Secondary 13A17, 14A05
MathSciNet review: 982402
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Abstract: We show that for every nonzero prime ideal $ P$ in a Noetherian domain $ R$ there are either just one or infinitely many prime ideals of the absolute integral closure of $ R$ lying over $ P$. Using this result we show that if $ R$ is a semilocal countable one-dimensional Noetherian domain, then there exist just two possibilities for the prime ideal spectrum of $ R[y]$, depending on whether or not $ R$ is Henselian.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0982402-3
PII: S 0002-9939(1989)0982402-3
Keywords: Prime ideal spectrum, polynomial ring, Noetherian ring, $ n$-split ideal, Henselian ring
Article copyright: © Copyright 1989 American Mathematical Society