# On generalizations of semiperfect and perfect rings

Document Type : Research Paper

Author

Department of Mathematics, Sinop University, 57000, Sinop, Turkey.

Abstract

‎We call a ring $R$ right generalized semiperfect if every simple right $R$-module is an epimorphic image of a flat right $R$-module with small kernel‎, ‎that is‎, ‎every simple right $R$-module has a flat $B$-cover‎. ‎We give some properties of such rings along with examples‎. ‎We introduce flat strong covers as flat covers which are also flat $B$-covers and give characterizations of $A$-perfect‎, ‎$B$-perfect and perfect rings in terms of flat strong covers.

Keywords

Main Subjects

#### References

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F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Grad. Texts in Math., 13, Springer-Verlag, New York, 1992.
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H. Bass, Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. 95 (1960) 466--488.
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F. Kasch, Modules and Rigs, London Math. Soc. Monogr. Ser. 17, Translated from German and edited by D. A. R. Wallace, Academic Press, London- New York, 1982.
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### History

• Receive Date: 02 July 2015
• Revise Date: 08 September 2015
• Accept Date: 15 September 2015