A property of weakly Krull domains
Authors:
D. D. Anderson and Muhammad Zafrullah
Journal:
Proc. Amer. Math. Soc. 131 (2003), 36893692
MSC (2000):
Primary 13F05
Published electronically:
April 30, 2003
MathSciNet review:
1998175
Fulltext PDF Free Access
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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 gradeone prime ideal of is of height one. We also show that a modification of can be used to characterize Noetherian domains that are onedimensional.
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 D.D. Anderson, J.L. Mott and M. Zafrullah, Finite character representations for integral domains, Boll. Un. Mat. Ital. B (7) 6 (1992), 613630. MR 93k:13001
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 V. Barucci, Mori domains, NonNoetherian Commutative Ring Theory, Math. Appl., vol. 520, Kluwer Acad. Publ., Dordrecht, 2000, pp. 5773. MR 2002h:13028
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 I. Kaplansky, Commutative Rings, University of Chicago Press, Chicago, IL, 1974, revised edition of the 1970 edition, Allyn and Bacon, Boston. MR 49:10674
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 M. Zafrullah, Putting invertibility to use, NonNoetherian Commutative Ring Theory, Math. Appl., vol. 520, Kluwer Acad. Publ., Dordrecht, 2000, pp. 429457. MR 2002g:13009
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Additional Information
D. D. Anderson
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email:
dananderson@uiowa.edu
Muhammad Zafrullah
Affiliation:
Department of Mathematics, Idaho State University, Pocatello, Idaho 832098085
Email:
mzafrullah@usa.net
DOI:
http://dx.doi.org/10.1090/S0002993903070473
PII:
S 00029939(03)070473
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
