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

DOI:
https://doi.org/10.1090/S0002-9939-03-07047-3

Published electronically:
April 30, 2003

MathSciNet review:
1998175

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Abstract: We show that a weakly Krull domain satisfies : for every pair there is an such that is -invertible. For Noetherian, satisfies if and only if every grade-one prime ideal of is of height one. We also show that a modification of 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:
https://doi.org/10.1090/S0002-9939-03-07047-3

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