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Generalizations of the Simple Torsion Class and the Splitting Properties

Published online by Cambridge University Press:  20 November 2018

Mark L. Teply
Mark L. Teply*
Affiliation:
University of Florida, Gainesville, Florida
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In this paper all rings R are associative rings with identity and all modules are members of R-mod, the category of unital left R-modules, unless the contrary is specifically stated.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 1056 - 1074
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Bass, H., Finitistic homologuai dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960), 466–488.Google Scholar
2. Dickson, S. E., A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1966), 223–235.Google Scholar
3. Dickson, S. E., Noetherian splitting rings are Artinian, J. London Math. Soc. 42 (1967), 732–736.Google Scholar
4. Fuchs, L., Torsion preradicals and ascending Loewy series of modules, J. Reine Angew. Math. 239/240 (1969), 169–179.Google Scholar
5. Fuelberth, J. D., On commutative splitting rings, Proc. London Math. Soc. 20 (1970), 393–408.Google Scholar
6. Fuelberth, J. D. and Teply, M. L., The singular submodule of a finitely generated module splits off, Pacific J. Math. 40 (1972), 73–82.Google Scholar
7. Golan, J. S., On the torsion-theoretic spectrum of a non-commutative ring (preprint, 1973).Google Scholar
8. Goodearl, K. R., Singular torsion and the splitting properties, Mem. Amer. Math. Soc. 124 (1972).Google Scholar
9. Gorbachuk, E. L., Splitting torsion and pretorsion in the category of right A-modules, Mat. Zametki 2 (1967), 681–688.Google Scholar
10. Gordon, R. and Robson, J. C., Krull dimension, Mem. Amer. Math. Soc. 133 (1973).Google Scholar
11. Kaplansky, I., Projective modules, Ann. of Math. 68 (1958), 372–377.Google Scholar
12. Lambek, J., Torsion theories, additive semantics, and rings of quotients, Lecture Notes in Mathematics 177 (Springer-Verlag, Berlin, 1971).Google Scholar
13. Shores, T. S., The Structure of Loewy modules, J. Reine Agnew. Math. 254 (1972), 204–220.Google Scholar
14. Stenstrom, B., Rings and modules of quotients, Lecture Notes in Mathematics 237 (Springer- Verlag, Berlin, 1971).Google Scholar
15. Teply, M. L., The torsion submodule of a cyclic module splits off, Can. J. Math 24 (1972), 450–464.Google Scholar
16. Teply, M. L., Onnon-commutative splitting rings, J. London Math. Soc. 4 (1971), 157-164. (See also Corrigendum in J. London Math. Soc. 6 (1973), 267–268.)Google Scholar
17. Teply, M. L. and Fuelberth, J. D., The torsion submodule splits off, Math. Ann. 188 (1970), 270–284.Google Scholar