Abstract
References
- Amini, A., Amini, B., Ershad, M. and Sharif, H., On generalized perfect rings, Comm. Algebra (2007), 35(3), 953--963.
- Amini, A., Ershad, M. and Sharif, H., Rings over which flat covers of finitely generated modules are projective, Comm. Algebra (2008), 36(8), 2862--2871.
- Anderson, F. W. and Fuller, K. R., Rings and Categories of Modules, Graduate Texts in Mathematics, Springer-Verlag, New York, 1992.
- Atiyah, M. F. and Macdonald, I. G., Introduction to commutative algebra, Addison-Wesley Publishing Co., London, 1969. aydougdu2013rings : Aydoğdu, P., Rings over which every module has a flat δ-cover, Turkish J. Math. (2013), 37(1), 182--194.
- Bass, H., Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. (1960), 95, 466--488.
- Büyükaşık, E., Rings over which flat covers of simple modules are projective, J. Algebra Appl. (2012), 11(3), 1250046.
- Büyükaşık, E. and Lomp, C., When δ-semiperfect rings are semiperfect, Turkish J. Math. (2010), 34(3):317--324.
- Demirci, Y. M., On generalizations of semiperfect and perfect rings, Bull. Iranian Math. Soc. (2016), 42(6), 1441--1450.
- Enochs, E. E., Injective and flat covers, envelopes and resolvents, Israel J. Math. (1981), 39(3), 189--209.
- Kasch, F., Modules and rings, London Mathematical Society Monographs, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1982. Translated from German with a preface by D. A. R. Wallace.
- Lam, T. Y., Lectures on Modules and Rings, Graduate Texts in Mathematics, Springer, New York, 1999.
- Lomp, C., On semilocal modules and rings, Comm. Algebra (1999), 27(4), 1921--1935.
- Xu, J., Flat covers of modules, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1996.
- Zhou, Y., Generalizations of perfect, semiperfect, and semiregular rings, Algebra Colloq. (2000), 7(3), 305--318.
Abstract
We say that a ring R is right generalized δ-semiperfect if every simple right R-module is an epimorphic image of a flat right R-module with δ-small kernel. This definition gives a generalization of both right δ-semiperfect rings and right generalized semiperfect rings. We provide examples involving such rings along with some of their properties. We introduce flat strong δ-cover of a module as a flat cover which is also a flat δ-cover and use flat strong δ-covers in characterizing right A-perfect rings, right B-perfect rings and right perfect rings.
Keywords
Flat cover flat δ-cover flat strong δ-cover G-δ-semiperfect ring semiperfect ring perfect ring
References
- Amini, A., Amini, B., Ershad, M. and Sharif, H., On generalized perfect rings, Comm. Algebra (2007), 35(3), 953--963.
- Amini, A., Ershad, M. and Sharif, H., Rings over which flat covers of finitely generated modules are projective, Comm. Algebra (2008), 36(8), 2862--2871.
- Anderson, F. W. and Fuller, K. R., Rings and Categories of Modules, Graduate Texts in Mathematics, Springer-Verlag, New York, 1992.
- Atiyah, M. F. and Macdonald, I. G., Introduction to commutative algebra, Addison-Wesley Publishing Co., London, 1969. aydougdu2013rings : Aydoğdu, P., Rings over which every module has a flat δ-cover, Turkish J. Math. (2013), 37(1), 182--194.
- Bass, H., Finitistic dimension and a homological generalization of semi-primary rings, Trans. Amer. Math. Soc. (1960), 95, 466--488.
- Büyükaşık, E., Rings over which flat covers of simple modules are projective, J. Algebra Appl. (2012), 11(3), 1250046.
- Büyükaşık, E. and Lomp, C., When δ-semiperfect rings are semiperfect, Turkish J. Math. (2010), 34(3):317--324.
- Demirci, Y. M., On generalizations of semiperfect and perfect rings, Bull. Iranian Math. Soc. (2016), 42(6), 1441--1450.
- Enochs, E. E., Injective and flat covers, envelopes and resolvents, Israel J. Math. (1981), 39(3), 189--209.
- Kasch, F., Modules and rings, London Mathematical Society Monographs, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1982. Translated from German with a preface by D. A. R. Wallace.
- Lam, T. Y., Lectures on Modules and Rings, Graduate Texts in Mathematics, Springer, New York, 1999.
- Lomp, C., On semilocal modules and rings, Comm. Algebra (1999), 27(4), 1921--1935.
- Xu, J., Flat covers of modules, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1996.
- Zhou, Y., Generalizations of perfect, semiperfect, and semiregular rings, Algebra Colloq. (2000), 7(3), 305--318.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Review Articles |
| Authors | |
| Publication Date | February 1, 2019 |
| Submission Date | April 2, 2017 |
| Acceptance Date | November 22, 2017 |
| Published in Issue | Year 2019 Volume: 68 Issue: 1 |
Cite
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
