Krull's principal ideal theorem in non-Noetherian settings
-
Published:2018-08-08
Issue:1
Volume:168
Page:13-27
-
ISSN:0305-0041
-
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
-
language:en
-
Short-container-title:Math. Proc. Camb. Phil. Soc.
Abstract
AbstractLetPbe a finitely generated ideal of a commutative ringR. Krull's principal ideal theorem states that ifRis Noetherian andPis minimal over a principal ideal ofR, thenPhas height at most one. Straightforward examples show that this assertion fails ifRis not Noetherian. We consider what can be asserted in the non-Noetherian case in place of Krull's theorem.
Publisher
Cambridge University Press (CUP)
Subject
General Mathematics
Reference25 articles.
1. Some counterexamples related to integral closure in D[[x]];Ohm;Trans. Amer. Math. Soc.,1966
2. S. Gabelli and M. Roitman Finitely stable domains, II Preprint.
3. Ideal Theory