A ring R is called right F-injective if every right R-homomorphism
from a finitely generated right ideal of R to R extends to an endomorphism
of R. R is called a right FSE-ring if R is a right F-injective semiperfect ring
with essential right socle. The class of right FSE-rings is broader than that of
right PF-rings. In this paper, we study and provide some characterizations of
this class of rings. We prove that if R is left perfect, right F-injective, then
R is QF if and only if R/S is left finitely cogenerated where S = Sr = Sl if
and only if R is left semiartinian, Soc2(R) is left finitely generated. It is also
proved that R is QF if and only if R is left perfect, mininjective and J2 = r(I)
for a finite subset I of R. Some known results are obtained as corollaries.

F(P)-injective ring, mininjective ring, finitely continuous ring, min-CS, QF-ring, PF-ring, FSE-ring, uniform module

- F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer Verlag, New York, 1974.
- J. E. Bj¨ork, Rings satisfying certain chain conditions, J. Reine Angew. Math. (1970), 63-73.
- J. Chen and N. Ding, On generalization of injective rings, In International Symposium on Ring Theory, South Korea, June 28-July 3, 1999.
- J. Chen and N. Ding, On general principally injective rings, Comm. Algebra, (5) (1999), 2097-2116.
- J. Chen, N. Ding and M. F. Yousif, On generalizations of PF-rings, Comm. Algebra, 32 (2) (2004), 521-533.
- N. V. Dung, D. V. Huynh, P. F. Smith and R. Wisbauer, Extending Modules, Pitman Research Notes in Math. 313, Longman, 1994.
- C. Faith, Algebra II: Ring Theory, Springer-Verlag, Berlin, 1976.
- C. Faith, When self-injective rings are QF: a report on a problem. Centre Recerca Matemtica Institut d’Estudis Catalans (Spain), 1990.
- C. Faith and D. V. Huynh, When self-injective rings are QF: A report on a problem, J. of Algebra and Its Appl. 1(1) (2002), 75-105.
- K.R Goodearl, Von Neumann Regular Rings, Pitman, London, 1979.
- K.R Goodearl, Ring Theory : Nonsingular Rings and Modules, Monographs Textbooks Pure Appl. Math. 33, 1975.
- K.R Goodearl and R. B. Warfield, An introduction to noncommutative Noe- therian rings, Cambridge Uni. Press, 1989.
- D. V. Huynh, P. Dan, On rings with restricted minimum conditions, Arch. Math. 51 (1988), 313-326.
- F. Kasch, Modules and Rings, Academic Press, London, New York, 1982.
- W.K. Nicholson and M.F. Yousif, Quasi-Frobenius Rings, Cambridge Univ. Press., 2003.
- W.K. Nicholson and M.F. Yousif, Principally injective rings, J. Algebra 174 (1995), 77-93.
- W.K. Nicholson and M.F. Yousif, Mininjective rings, J. Algebra 187 (1997), 578.
- W.K. Nicholson and M.F. Yousif, Annihilators and the CS-condition, Glasgow Math. J. 40(2) (1998) 213-222.
- T. C. Quynh and L. V. Thuyet, On rings with ACC on annihilators and having essential socles, to appear in The Procceding of Bangkok (2006).
- E. A. JR. Rutter, Rings with the principal extension property, Comm. Algebra, (3) (1975), 203-212.
- L. D. Thoang and L. V. Thuyet, On semiperfect mininjective rings with essen- tial socles, The Southeast Asian Bulletin of Mathematics, 30 (2006), 555-560.
- L. V. Thuyet, On continuous rings with chain conditions, Vietnam J. Math. (1) (1991), 49 - 59.
- L. V. Thuyet and R. Wisbauer, Extending property for finitely generated sub- modules, Vietnam J. Math. 25(1) (1997), 65 - 73.
- R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Truong Cong Quynh Department of Mathematics, Hue University, Vietnam e-mail: matht2q2004@hotmail.com

Konular | |
---|---|

Diğer ID | JA24PG26HZ |

Dergi Bölümü | Makaleler |

Yazarlar |

Bibtex | ```
@ { ieja266412,
journal = {International Electronic Journal of Algebra},
issn = {1306-6048},
eissn = {1306-6048},
address = {Prof. Dr. Abdullah HARMANCI},
year = {2007},
volume = {1},
pages = {18 - 29},
doi = {},
title = {ON SEMIPERFECT F-INJECTIVE RINGS},
key = {cite},
author = {Quynh, Truong Cong}
}
``` |

APA | Quynh, T . (2007). ON SEMIPERFECT F-INJECTIVE RINGS. International Electronic Journal of Algebra, 1 (1), 18-29. Retrieved from http://dergipark.gov.tr/ieja/issue/25210/266412 |

MLA | Quynh, T . "ON SEMIPERFECT F-INJECTIVE RINGS". International Electronic Journal of Algebra 1 (2007): 18-29 <http://dergipark.gov.tr/ieja/issue/25210/266412> |

Chicago | Quynh, T . "ON SEMIPERFECT F-INJECTIVE RINGS". International Electronic Journal of Algebra 1 (2007): 18-29 |

RIS | TY - JOUR T1 - ON SEMIPERFECT F-INJECTIVE RINGS AU - Truong Cong Quynh Y1 - 2007 PY - 2007 N1 - DO - T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 18 EP - 29 VL - 1 IS - 1 SN - 1306-6048-1306-6048 M3 - UR - Y2 - 2019 ER - |

EndNote | %0 International Electronic Journal of Algebra ON SEMIPERFECT F-INJECTIVE RINGS %A Truong Cong Quynh %T ON SEMIPERFECT F-INJECTIVE RINGS %D 2007 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 1 %N 1 %R %U |

ISNAD | Quynh, Truong Cong . "ON SEMIPERFECT F-INJECTIVE RINGS". International Electronic Journal of Algebra 1 / 1 (Haziran 2007): 18-29. |