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On maxi-quasiprojective modules

Published online by Cambridge University Press:  09 April 2009

Manabu Harada
Manabu Harada
Affiliation:
Osaka City UniversitySumiyoshi-KuOsaka 558, Japan
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Abstract

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We have defined a mini-injective module and given some structures of self mini-injective rings and certain relationships between such rings and QF-rings in [8] and [9].

In this short note we shall study the modules dual to mini-injective modules, which we call maxi-quasiprojective modules. We shall give a characterization and some structures, in terms of the above modules, of those rings whose every injective modules has the lifting property of direct decompositions modulo the Jacobian radical (see [5], [6] and [7]). Furthermore, we shall show that the above rings are closely related to QF-rings (see [8] and [9]).

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 3 , December 1983 , pp. 357 - 368
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Asashiba, H. and Sumioka, T., ‘On Krull-Schmidt's theorem and the indecomposability of amalgamated sums,’ to appear.Google Scholar
[2]Eilenberg, S. and Nakayama, T., ‘On the dimension of modules and algebras II’, Nagoya Math. J. 9 (1956), 1–16.CrossRefGoogle Scholar
[3]Harada, M., ‘Non-small modules and non-cosmall modules’, Proc. of Ring Theory 1978, pp. 669–689 (Antwerp, Marcel Dekker, New York).Google Scholar
[4]Harada, M., ‘Note on quasi-injective modules’, Osaka J. Math 2 (1965), 351–356.Google Scholar
[5]Harada, M., ‘On one-sided QF-2 rings I’, Osaka J. Math. 17 (1980), 421–431.Google Scholar
[6]Harada, M., ‘On lifting property on direct sums of hollow modules’, Osaka J. Math. 17 (1980), 783–791.Google Scholar
[7]Harada, M., ‘On modules with lifting properties’, Osaka J. Math. 19 (1982), 189–201.Google Scholar
[8]Harada, M., ‘Self mini-injective rings’, Osaka J. Math. 19 (1982), 587–597.Google Scholar
[9]Harada, M., ‘A characterization of QF-rings’, to appear.Google Scholar
[10]Jans, J. P. and Wu, L. E., ‘On quasi-projectives’, Illnois J. Math. 11 (1967), 439–448.Google Scholar
[11]Kanbara, H., ‘Note on Krull-Remak-Schmidt-Azumaya's theorem’, Osaka J. Math. 9 (1972), 409–413.Google Scholar
[12]Mares, E., ‘Semi-perfect modules’, Math. Z. 83 (1963), 347–360.CrossRefGoogle Scholar
[13]Morita, K., ‘Duality for modules and its applications to the theory of rings with minimum conditions’, Sci. Rep. Tokyo. Kyoiku Daigaku Sect. A (1958), 83–142Google Scholar
[14]Oshima, M., ‘Notes on basic rings’, Math. J. Okayama Univ. 2 (1952–1953), 103–110.Google Scholar
[15]Nakayama, T., ‘On Frobenius algebras II’, 42 (1941), 1–21.Google Scholar
[16]Warfield, R. B. Jr, ‘Decompositions of injective modules’, Pacific J. Math. 31 (1969), 263–276.CrossRefGoogle Scholar