Note on simple integral extension domains and maximal chains of prime ideals

Ratliff, L. J.

doi:10.1090/S0002-9939-1979-0542081-X

Note on simple integral extension domains and maximal chains of prime ideals
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Proc. Amer. Math. Soc. 77 (1979), 179-185 Request permission

Abstract:

It is shown that if R is a semi-local (Noetherian) domain, then there exists a simple integral extension domain $R[e]$ of R such that there exists a maximal chain of prime ideals of length n in some integral extension domain of R if and only if there exists a maximal chain of prime ideals of length n in $R[e]$. An interesting existence theorem on a certain type of height one prime ideals in $R[X]$ follows.

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On maximal ideals and simple integral extension rings