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

 

Composition series of modules
over Prüfer domains


Author: Bruce Olberding
Journal: Proc. Amer. Math. Soc. 127 (1999), 1917-1921
MSC (1991): Primary 13F05, 13C05; Secondary 15A75, 20K15
Published electronically: February 17, 1999
MathSciNet review: 1487333
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Abstract | References | Similar Articles | Additional Information

Abstract: A weakened version of the Jordan-Hölder theorem is shown to hold for torsion-free finite rank modules over an integral domain $R$ precisely when $R$ is a Prüfer domain.


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Additional Information

Bruce Olberding
Affiliation: Department of Mathematics, Northeast Louisiana University, Monroe, Louisiana 71209
Email: maolberding@alpha.nlu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04760-7
PII: S 0002-9939(99)04760-7
Keywords: Pr\"{u}fer domain, torsion-free module, exterior algebra
Received by editor(s): April 12, 1997
Received by editor(s) in revised form: September 24, 1997
Published electronically: February 17, 1999
Additional Notes: Some of these results appeared in the author’s Ph.D. dissertation, which was written under the supervision of Professor J. D. Reid at Wesleyan University
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1999 American Mathematical Society