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Simple Divisible Modules Over Integral Domains

Published online by Cambridge University Press:  20 November 2018

Alberto Facchini
Alberto Facchini*
Affiliation:
Dipartimento di Matematica e Informatica, Universita' di Udine, 33100 Udine, Italy
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Abstract

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An R-module is a simple divisible module if it is a nonzero divisible module that has no proper non-zero divisible submodules. We study simple divisible modules and their endomorphism rings, give some examples and determine all simple divisible modules over some classes of rings.

Keywords

13C1313G05Divisible modulesModules over integral domains

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 2 , 01 June 1989, pp. 230 - 240
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Bazzoni, S. and Salce, L., On non-standard uniserial modules over valuation domains and their quotients, to appear in J. Algebra.Google Scholar
2. Claborn, L., Every abelian group is a class group, Pacific J. Math. 18 (1966), pp. 219-222.Google Scholar
3. Franzen, B. and Gobel, R., Nonstandard uniserial modules over valuation domains, Results in Math. 12 (1987), pp. 86-94.Google Scholar
4. Fuchs, L. and Salce, L., Modules over valuation domains, Marcel Dekker, New York-Basel, 1985.Google Scholar
5. Lee, S. B., On divisible modules over domains, Arch. Math, to appear.Google Scholar
6. Matlis, E., Some properties of Noetherian domains of dimension one, Canadian J. Math. 13 (1961), pp. 569-586.Google Scholar
7. Matlis, E., Torsion-free modules, Univ. of Chicago Press, Chicago-London, 1972.Google Scholar
8. Matlis, E., 1-Dimensional Cohen-Macaulay Rings, Lecture Notes in Mathematics 327,Springer- Verlag, Berlin-Heidelberg-New York, 1973.Google Scholar
9. Sharpe, D. W. and Varnos, P., Injective modules, Cambridge Univ. Press, Cambridge, 1972.Google Scholar
10. Shelah, S., Non standard uniserial module over a uniserial domain exists, in Around Classification Theory of Models, Lecture Notes in Math. 1182, Springer-Verlag, Berlin-Heidelberg-New York, 1986, pp. 135–150.Google Scholar
11. Shores, T. S. and Lewis, W. J., Serial modules and endomorphism rings, Duke Math. J. 41 (1974), pp. 889-909.Google Scholar
12. Varnos, P., Classical rings, J. Algebra 34 (1975), pp. 114-129.Google Scholar
13. Vasconcelos, W. V., Conductor, projectivity and injectivity, Pacific J. Math. 46 (1973), pp. 603-608.Google Scholar