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## ON SEMIPERFECT F-INJECTIVE RINGS

#### Truong Cong Quynh [1]

##### 67 130

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
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Other ID JA24PG26HZ Articles Author: Truong Cong Quynh Publication Date: June 1, 2007
 Bibtex @ { ieja266412, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {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.org.tr/ieja/issue/25210/266412 MLA Quynh, T . "ON SEMIPERFECT F-INJECTIVE RINGS". International Electronic Journal of Algebra 1 (2007): 18-29 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 (June 2007): 18-29. AMA Quynh T . ON SEMIPERFECT F-INJECTIVE RINGS. IEJA. 2007; 1(1): 18-29. Vancouver Quynh T . ON SEMIPERFECT F-INJECTIVE RINGS. International Electronic Journal of Algebra. 2007; 1(1): 29-18.