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Quasi-dual-continuous modules

Published online by Cambridge University Press:  09 April 2009

Saad Mohamed ,
Bruno J. Müller  and
Surjeet Singh
Saad Mohamed
Affiliation:
Department of Mathematics, Kuwait University, Kuwait
Bruno J. Müller
Affiliation:
Department of Mathematics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada
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Abstract

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Quasi-dual-continuous modules, which generalize the concept of dual-continuous modules, are studied Mohamed, Müller and Singh had obtained some decomposition theorems and their partial converses for dual-continuous modules. It is shown that these results can be extended to quasi-dual-continuous modules. Further, a short proof of a decomposition theorem for quasi-dual-continuous modules established recently by Oshiro is given. Some more structure theorems for such modules are established. Finally, quasi-dual-continuous covers are studied, and duals for results of Müller and Rizvi are derived.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 3 , December 1985 , pp. 287 - 299
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Anderson, F. W. and Fuller, K. R., Rings and categories of modules (Graduate Texts in Mathematics 13, Springer-Verlag, 1973).Google Scholar
[2]Azumaya, G., ‘M–projective and M–injective modules’, unpublished.Google Scholar
[3]Azumaya, G., Mbumtum, F. and Varadarajan, K., ‘On M–projective and M–injective modules’, Pacific J. Math. 95 (1975), 9–16.CrossRefGoogle Scholar
[4]Bass, H., ‘Finitistic dimension and homological generalization of semiprimary rings’, Trans. Amer. Math. Soc. 95 (1960), 466–488.CrossRefGoogle Scholar
[5]Jeremy, L., ‘Modules et anneux quasi-continus’, Canad. Math. Bull. 17 (1974), 217–228.CrossRefGoogle Scholar
[6]Mares, E. A., ‘Semi-perfect modules’, Math. Z. 82 (1963), 347–360.CrossRefGoogle Scholar
[7]Miyashita, Y., ‘Quasi-projective modules, perfect modules and a theorem for modular lattices’, J. Fac. Sci. Hokkaido Univ. 19 (1966), 88–110.Google Scholar
[8]Mohamed, S., ‘Rings with dual continuous right ideals’, J. Austral. Math. Soc. 33 (1982), 287–294.CrossRefGoogle Scholar
[9]Mohamed, S. and Abdel-Karim, F. H. A., ‘Semi-dual continuous abelian groups’, J. Kuwait Univ. (Sci.), to appear.Google Scholar
[10]Mohamed, S. and Bouhy, T., ‘Continuous modules’, Arabian J. Sci. and Engrg. 2 (1977), 107–112.Google Scholar
[11]Mohamed, S. and Müller, B. J., Decomposition of dual-continuous modules, pp. 87–94, Module Theory, Proceedings (Seattle 1977) (Lecture Notes in Mathematics, Springer-Verlag, 700 (1979)).Google Scholar
[12]Mohamed, S. and Müller, B. J., ‘Direct sums of dual continuous modules’, Math. Z. 178 (1981), 225–232.CrossRefGoogle Scholar
[13]Mohamed, S. and Singh, S., ‘Generalizations of decomposition theorems known over perfect rings’, J. Austral. Math. Soc. 24 (1977), 496–510.CrossRefGoogle Scholar
[14]Müller, B. J. and Rizvi, S. T., ‘On injective and quasi-continuous modules’, J. Pure Appl. Algebra 28 (1983), 197–210.CrossRefGoogle Scholar
[15]Oshiro, K., ‘Semi-perfect modules and quasi-semi-perfect modules’, Osaka J. Math. 20 (1983), 337–372.Google Scholar
[16]Singh, S., ‘Dual continuous modules over Dedekind domains’, J. Univ. Kuwait (Sci.) 7 (1980), 1–9.Google Scholar
[17]Singh, S., ‘Semi-dual continuous modules over Dedekind domains’, J. Univ. Kuwait (Sci.), to appear.Google Scholar
[18]Utumi, Y., ‘On continuous rings and self-injective rings’, Trans. Amer. Math. Soc. 118 (1965), 158–173.CrossRefGoogle Scholar
[19]Warfield, R. B., ‘A Krull-Schmidt theorem for infinite sums of modules’, Proc. Amer. Math. Soc. 22 (1969), 460–465.CrossRefGoogle Scholar
[20]Wu, L. E. T. and Jans, J. P., ‘On quasi-projectives’, Illinois J. Math. 11 (1967), 439–447.CrossRefGoogle Scholar