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Krull's principal ideal theorem in non-Noetherian settings

Published online by Cambridge University Press:  08 August 2018

BRUCE OLBERDING
BRUCE OLBERDING*
Affiliation:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003-8001, U.S.A. e-mail: olberdin@nmsu.edu
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Abstract

Let P be a finitely generated ideal of a commutative ring R. Krull's principal ideal theorem states that if R is Noetherian and P is minimal over a principal ideal of R, then P has height at most one. Straightforward examples show that this assertion fails if R is not Noetherian. We consider what can be asserted in the non-Noetherian case in place of Krull's theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 1 , January 2020 , pp. 13 - 27
Copyright
Copyright © Cambridge Philosophical Society 2018 

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