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

 

A property of weakly Krull domains


Authors: D. D. Anderson and Muhammad Zafrullah
Journal: Proc. Amer. Math. Soc. 131 (2003), 3689-3692
MSC (2000): Primary 13F05
Published electronically: April 30, 2003
MathSciNet review: 1998175
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Abstract: We show that a weakly Krull domain $D$ satisfies $(\ast )$: for every pair $ a,b\in D\backslash \{0\}$ there is an $n=n(a,b)\in \mathbb{N} $ such that $ (a,b^{n})$ is $t$-invertible. For $D$ Noetherian, $D$ satisfies $(\ast )$ if and only if every grade-one prime ideal of $D$ is of height one. We also show that a modification of $(\ast )$ can be used to characterize Noetherian domains that are one-dimensional.


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Additional Information

D. D. Anderson
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email: dan-anderson@uiowa.edu

Muhammad Zafrullah
Affiliation: Department of Mathematics, Idaho State University, Pocatello, Idaho 83209-8085
Email: mzafrullah@usa.net

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07047-3
PII: S 0002-9939(03)07047-3
Keywords: Weakly Krull
Received by editor(s): August 12, 2002
Published electronically: April 30, 2003
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2003 American Mathematical Society