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Composition series of modules over Prüfer domains
Author(s):
Bruce
Olberding
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1917-1921.
MSC (1991):
Primary 13F05, 13C05;
Secondary 15A75, 20K15
Posted:
February 17, 1999
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Abstract:
A weakened version of the Jordan-Hölder theorem is shown to hold for torsion-free finite rank modules over an integral domain  precisely when  is a Prüfer domain.
References:
- 1.
- R. A. Beaumont and R. S. Pierce, Torsion-free groups of rank two, Mem. Amer. Math. Soc. 72 (1961). MR 24:A162
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- N. Bourbaki, Elements of mathematics: Algebra I, Chapters 1 - 3, Springer-Verlag, 1989. MR 90d:00002
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- L. Fuchs and L. Salce, Modules over valuation domains, Lecture notes in pure and applied mathematics 96, Marcel Dekker, New York, 1985. MR 86h:13008
- 4.
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- 5.
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- O. Mutzbauer, Type invariants of torsion-free abelian groups, Contemporary Math. 87 (1989), 133-154. MR 90c:20069
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Additional Information:
Bruce
Olberding
Affiliation:
Department of Mathematics, Northeast Louisiana University, Monroe, Louisiana 71209
Email:
maolberding@alpha.nlu.edu
DOI:
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
Posted:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
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