Composition series of modules over Prüfer domains
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- by Bruce Olberding PDF
- Proc. Amer. Math. Soc. 127 (1999), 1917-1921 Request permission
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
- R. A. Beaumont and R. S. Pierce, Torsion free groups of rank two, Mem. Amer. Math. Soc. 38 (1961), 41. MR 130297
- 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
- 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
- Robert B. Gardner, Lectures on exterior algebras over commutative rings, University of North Carolina, Department of Mathematics, Chapel Hill, N.C., 1972. MR 0407056
- 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
- Akira Hattori, The solution of problem 6.1.13, Sūgaku 8 (1956/57), 207–208 (Japanese). MR 94335
- Daniel Lazard, Autour de la platitude, Bull. Soc. Math. France 97 (1969), 81–128 (French). MR 254100, DOI 10.24033/bsmf.1675
- Otto Mutzbauer, Type graph, Abelian group theory (Honolulu, Hawaii, 1983) Lecture Notes in Math., vol. 1006, Springer, Berlin, 1983, pp. 228–252. MR 722621, DOI 10.1007/BFb0103705
- 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, DOI 10.1090/conm/087/995271
- Joseph Rotman, The Grothendieck group of torsion-free abelian groups of finite rank, Proc. London Math. Soc. (3) 13 (1963), 724–732. MR 154913, DOI 10.1112/plms/s3-13.1.724
- J. J. Rotman, An introduction to homological algebra, Academic Press, 1979.
Additional Information
- Bruce Olberding
- Affiliation: Department of Mathematics, Northeast Louisiana University, Monroe, Louisiana 71209
- MR Author ID: 333074
- Email: maolberding@alpha.nlu.edu
- 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
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1487333