Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13A15, 13B99, 13F10

Retrieve articles in all journals with MSC: 13A15, 13B99, 13F10

Additional Information

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