A primary decomposition for torsion modules
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- by J. S. Alin PDF
- Proc. Amer. Math. Soc. 27 (1971), 43-48 Request permission
Abstract:
A definition of primary module is given and a theorem is proved characterizing rings for which each torsion module, in the sense of S. E. Dickson, decomposes as a direct sum of its primary submodules. This theorem is applied to obtain a generalization of Fuchs’ theorem on the additive group structure of Artinian rings.References
- J. S. Alin, Primary decomposition of modules, Math. Z. 107 (1968), 319–325. MR 238898, DOI 10.1007/BF01110064
- Spencer E. Dickson, Decomposition of modules. I. Classical rings, Math. Z. 90 (1965), 9–13. MR 184974, DOI 10.1007/BF01112047
- Spencer E. Dickson, Decomposition of modules. II. Rings without chain conditions, Math. Z. 104 (1968), 349–357. MR 229678, DOI 10.1007/BF01110426
- Spencer E. Dickson, A torsion theory for Abelian categories, Trans. Amer. Math. Soc. 121 (1966), 223–235. MR 191935, DOI 10.1090/S0002-9947-1966-0191935-0
- L. Fuchs, Abelian groups, International Series of Monographs on Pure and Applied Mathematics, Pergamon Press, New York-Oxford-London-Paris, 1960. MR 0111783 S. Mac Lane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #122.
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 43-48
- MSC: Primary 16.40
- DOI: https://doi.org/10.1090/S0002-9939-1971-0274496-4
- MathSciNet review: 0274496