Prime ideals in two-dimensional polynomial rings

Heinzer, William; Wiegand, Sylvia

doi:10.1090/S0002-9939-1989-0982402-3

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.

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