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Q-Divisible Modules

Published online by Cambridge University Press:  20 November 2018

Efraim P. Armendariz
Efraim P. Armendariz*
Affiliation:
The University of Texas at Austin, Austin, Texas
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Let R be a ring with 1 and let Q denote the maximal left quotient ring of R [6]. In a recent paper [12], Wei called a (left). R-module M divisible in case HomR (Q, N)≠0 for each nonzero factor module N of M. Modifying the terminology slightly we call such an R-module a Q-divisible R-module. As shown in [12], the class D of all Q-divisible modules is closed under factor modules, extensions, and direct sums and thus is a torsion class in the sense of Dickson [5].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 4 , December 1971 , pp. 491 - 494
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Armendariz, E. P., On finite-dimensional torsion-free modules and rings, Proc. Amer. Math. Soc. 24(1970), 566-571.Google Scholar
2. Bass, H., Finitistic dimension and a homological generalization of semiprimary rings, Trans. Amer. Math. Soc. 95 (1960), 466-480.Google Scholar
3. Cartan, H. and Eilenberg, S., Homological Algebra, Princeton Univ. Press, 1956.Google Scholar
4. Chase, S., Direct products of modules, Trans. Amer. Math. Soc. 97 (1960), 457-573.Google Scholar
5. Dickson, S. E., A torsion theory for Abelian categories, Trans. Amer. Math. Soc. 121 (1966), 223-235.Google Scholar
6. Lambek, J., Lectures on Rings and Modules, Blaisdell, Waltham, Mass., 1966.Google Scholar
7. Matlis, E., Divisible modules, Proc. Amer. Math. Soc. 11 (1960), 385-391.Google Scholar
8. Sandomierski, F., Semisimple maximal quotient rings, Trans. Amer. Math. Soc. 128 (1967), 112-120.Google Scholar
9.Sandomierski, F., rings, Nonsingular, Proc. Amer. Math. Soc. 19 (1968), 225-230.Google Scholar
10. Storrer, H., Rings of quotients of perfect rings (to appear).Google Scholar
11. Teply, M., Some aspects of Goldie's torsion theory, Pacific J. Math. 29 (1969), 447-460.Google Scholar
12. Wei, D., On the concept of torsion and divisibility for general rings, III. J. Math. 13 (1969), 414-431.Google Scholar