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

 

Simple going down in PI rings


Author: Phillip Lestmann
Journal: Proc. Amer. Math. Soc. 63 (1977), 41-45
MSC: Primary 13A15; Secondary 13B99, 13F10
MathSciNet review: 0432619
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Abstract: In this paper we prove two generalizations of a theorem which McAdam proved for commutative rings. Theorem 1 states that if $ R \subset S$ is a central integral extension of PI rings, then going down for prime ideals holds between R and S if and only if going down holds in $ R \subset R[s]$ for each $ s \in S$. Theorem 2 gives the analogous result for going down in $ C \subset R$ where C is a central subring of the PI ring R. As a corollary we obtain a result of Schelter generalizing Krull's theorem on going down for integral extensions of integrally-closed subrings.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0432619-3
PII: S 0002-9939(1977)0432619-3
Keywords: PI ring, going down, simple going down, integral, extension, going up, lying over, incomparability
Article copyright: © Copyright 1977 American Mathematical Society