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Reflexive Modules Over QF-3 Rings

Published online by Cambridge University Press:  20 November 2018

Kanzo Masaike*
Affiliation:
Department of Mathematics Tokyo Gakugei University Koganei, Tokyo 184 Japan
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Abstract

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We give a characterization of reflexive modules over QF-3 rings generalizing the concept of linearly compact modules. Further, we study necessary and sufficient conditions for left QF-3 rings to be right QF-3.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1992 

References

1. Colby, R. R. and Rutter, E. A. Jr., Generalization of QF-3 algebras, Trans. Amer. Math. Soc. 153(1971), 371386.Google Scholar
2. Kasch, F. and Mares, E. A., Eine Kennzeichnung semi-perfekter Moduln, Nagoya Math. J. 27(1966), 525 529.Google Scholar
3. Masaike, K., Duality for quotient modules and a characterization of reflexive modules, J. Pure and Applied Algebra 28(1983) 265277.Google Scholar
4. Morita, K., Duality in QF-3 rings, Math. Z. 108(1968), 237252.Google Scholar
5. Miiller, B. J., Linearly compactness and Morita duality, J. Algebra 16(1-70), 6066.Google Scholar
6. Ringel, C. M. and Tachikawa, H., QF-3 rings, J. Reine Angew. Math. 272(1975), 4972.Google Scholar
7. Rutter, E. A. Jr., Dominant modules and finite localizations, Tôhoku Math. J. 27(1975), 225239.Google Scholar
8. Sandomierski, F. L., Linearly compact modules and local Morita duality, Ring Theory, pp. 333-346, edited by Gordon, R., Academic Press N.Y. and London, 1972.Google Scholar
9. Stenstrôm, B., Rings of Quotient, Grund. Math. Wiss. 217 Springer-Verlag, Berlin, 1975.Google Scholar
10. Tachikawa, H., Quasi-Frobenius Rings and Generalizations, Lecture Notes in Math. 351 Springer-Verlag, Berlin, 1973.Google Scholar
11. Zelinsky, D., Linearly compact modules and rings, Amer. J. Math. 75(1953), 7990.Google Scholar