Prime ideals in two-dimensional polynomial rings
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- by William Heinzer and Sylvia Wiegand PDF
- Proc. Amer. Math. Soc. 107 (1989), 577-586 Request permission
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.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 577-586
- MSC: Primary 13B25; Secondary 13A17, 14A05
- DOI: https://doi.org/10.1090/S0002-9939-1989-0982402-3
- MathSciNet review: 982402