A property of weakly Krull domains
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- by D. D. Anderson and Muhammad Zafrullah PDF
- Proc. Amer. Math. Soc. 131 (2003), 3689-3692 Request permission
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.References
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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
- Received by editor(s): August 12, 2002
- Published electronically: April 30, 2003
- Communicated by: Bernd Ulrich
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3689-3692
- MSC (2000): Primary 13F05
- DOI: https://doi.org/10.1090/S0002-9939-03-07047-3
- MathSciNet review: 1998175