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

DOI:
https://doi.org/10.1090/S0002-9939-99-04760-7

Published electronically:
February 17, 1999

MathSciNet review:
1487333

Full-text PDF

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 precisely when is a Prüfer domain.

**1.**R. A. Beaumont and R. S. Pierce,*Torsion-free groups of rank two*, Mem. Amer. Math. Soc.**72**(1961). MR**24:A162****2.**N. Bourbaki,*Elements of mathematics: Algebra I, Chapters 1 - 3*, Springer-Verlag, 1989. MR**90d:00002****3.**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.**R. B. Gardner,*Exterior algebras over commutative rings*, University of North Carolina at Chapel Hill, 1972. MR**53:10839****5.**R. W. Gilmer,*Multiplicative Ideal Theory*, Queen's Papers in Pure and Applied Mathematics**90**, Queen's University, 1992. MR**93j:13001****6.**A. Hattori,*On Prüfer rings*, J. Math. Soc. Japan**9**(1957), 381-385. MR**20:854b****7.**D. Lazard,*Autour de la platitude*, Bull. Soc. Math. France**97**(1969), 81-128. MR**40:7310****8.**O. Mutzbauer,*Type graph*, Springer-Verlag Lecture Notes 1006, 228-252. MR**85d:20052****9.**O. Mutzbauer,*Type invariants of torsion-free abelian groups*, Contemporary Math.**87**(1989), 133-154. MR**90c:20069****10.**J. J. Rotman,*The Grothendieck group of torsion-free abelian groups of finite rank*, Proc. London Math. Soc. (3)**13**(1963), 724-732. MR**27:4857****11.**J. J. Rotman,*An introduction to homological algebra*, Academic Press, 1979.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
13F05,
13C05,
15A75,
20K15

Retrieve articles in all journals with MSC (1991): 13F05, 13C05, 15A75, 20K15

Additional Information

**Bruce Olberding**

Affiliation:
Department of Mathematics, Northeast Louisiana University, Monroe, Louisiana 71209

Email:
maolberding@alpha.nlu.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-04760-7

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