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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.

References [Enhancements On Off] (What's this?)

  • 1. R. A. Beaumont and R. S. Pierce, Torsion free groups of rank two, Mem. Amer. Math. Soc. No. 38 (1961), 41. MR 0130297
  • 2. Nicolas Bourbaki, Algebra. I. Chapters 1–3, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1989. Translated from the French; Reprint of the 1974 edition. MR 979982
  • 3. László Fuchs and Luigi Salce, Modules over valuation domains, Lecture Notes in Pure and Applied Mathematics, vol. 97, Marcel Dekker, Inc., New York, 1985. MR 786121
  • 4. Robert B. Gardner, Lectures on exterior algebras over commutative rings, Department of Mathematics, University of North Carolina, Chapel Hill, N. C., 1972. MR 0407056
  • 5. Robert Gilmer, Multiplicative ideal theory, Queen’s Papers in Pure and Applied Mathematics, vol. 90, Queen’s University, Kingston, ON, 1992. Corrected reprint of the 1972 edition. MR 1204267
  • 6. Akira Hattori, On Prüfer rings, J. Math. Soc. Japan 9 (1957), 381–385. MR 0094336
  • 7. Daniel Lazard, Autour de la platitude, Bull. Soc. Math. France 97 (1969), 81–128 (French). MR 0254100
  • 8. Otto Mutzbauer, Type graph, Abelian group theory (Honolulu, Hawaii, 1983) Lecture Notes in Math., vol. 1006, Springer, Berlin, 1983, pp. 228–252. MR 722621, 10.1007/BFb0103705
  • 9. Otto Mutzbauer, Type invariants of torsion-free abelian groups, Abelian group theory (Perth, 1987) Contemp. Math., vol. 87, Amer. Math. Soc., Providence, RI, 1989, pp. 133–154. MR 995271, 10.1090/conm/087/995271
  • 10. Joseph Rotman, The Grothendieck group of torsion-free abelian groups of finite rank, Proc. London Math. Soc. (3) 13 (1963), 724–732. MR 0154913
  • 11. J. J. Rotman, An introduction to homological algebra, Academic Press, 1979.

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Additional Information

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

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