On Composition Series of a Module with Respect to a Set of Gabriel Topologies
Composition series for modules with respect to a Gabriel topology (or equivalently, with respect to a hereditary torsion theory) were introduced by Goldman  in 1975, but only for torsion-free modules, and have been further studied, among others, by Beachy, Golan,etc.
KeywordsExact Sequence Finite Length Noetherian Ring Modular Lattice Torsion Theory
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- Albu, T. Certain artinian lattices are noetherian. Applications to the relative Hopkins-Levitzki theorem, in Methods -in Ring Theory, Van Oystaeyen, F., Editor, D. Reidel Publishing Company, Dordrecht-Holland, 1984.Google Scholar
- Boyle, A.K. and Feller, E.H. Semicritical modules and k-primitive rings, in Module. Theory, Lecture Notes in Mathematics 700, Springer-Verlag, Berlin Heidelberg New York, 1979.Google Scholar
- Nastasescu, C. Teria Dimensiunii in Algebra Necomutatlvà, Editura Academiei, Bucuresti, 1983.Google Scholar
- Teply, M.L. Composition series for sets of torsion theories, Abstracts. Math.Soc, 3, 274, 1982.Google Scholar
- Teply, M.L. Torsionfree modules and the semicritical socle series, preprint, 1983.Google Scholar