On Generalizations of PF-Rings

References

• Anderson , F. W. and Fuller , K. R. 1974 . Rings and Categories of Modules New York : Springer-Verlag .
   Google Scholar
• Armendariz , E. P. and Park , J. K. 1992 . Self-injective rings with restricted chain conditions . Arch. Math. , 58 : 24 – 33 .
   Google Scholar
• Björk , J.-E. 1970 . Rings satisfying certain chain conditions . J. Reine Angew. Math. , 245 : 63 – 73 .
   Google Scholar
• Camillo , V. , Nicholson , W. K. and Yousif , M. F. 2000 . Ikeda-Nakayama rings . J. Algebra , 226 : 1001 – 1010 . [CROSSREF]
   Google Scholar
• Chen , J. and Ding , N. 1999 . On general principally injective rings . Comm. Algebra , 27 ( 5 ) : 2097 – 2116 .
   Google Scholar
• Chen , J. and Ding , N. On generalizations of injectivity . International Symposium on Ring Theory . June 28–July 3 1999 , South Korea . Edited by: Birkenmeier , G. F. , Park , J. K. and Park , Y. S. pp. 85 – 94 . Boston : Birkhäuser .
   Google Scholar
• Chen , J. , Ding , N. , Li , Y. and Zhou , Y. 2001 . On (m, n)-injectivity of modules . Comm. Algebra , 29 ( 12 ) : 5589 – 5603 . [CROSSREF]
   Google Scholar
• Clark , J. and Huynh , D. V. 1994a . A note on perfect self-injective rings . Quart. J. Math. Oxford , 45 ( 2 ) : 13 – 17 .
   Google Scholar
• Clark , J. and Huynh , D. V. 1994b . When is a self-injective semiperfect ring quasi- Frobenius? . J. Algebra , 165 : 531 – 542 . [CROSSREF]
   Google Scholar
• Faith , C. 1976 . Algebra II – Ring Theory New York : Springer-Verlag .
   Google Scholar
• Faith , C. 1990 . When self-injective rings are QF: A report on a problem. Centre Recerca Matemàtica Institut d'Estudis Catalans (Spain)
   Google Scholar
• Goodearl , K. R. 1976 . Ring Theory: Nonsingular Rings and Modules , Monographs Textbooks Pure Appl. Math. Vol. 33 , New York and Basel : Marcel Dekker, Inc. .
   Google Scholar
• Goodearl , K. R. and Warfield , R. B. Jr. 1989 . An Introduction to Noncommutative Noetherian Rings , London Mathematical Society Student Texts 16 Cambridge University Press .
   Google Scholar
• Gómez Pardo , J. L. and Guil Asensio , P. A. 1998 . “ Torsionless modules and rings with finite essential socle. ” . In Abelian groups Module Theory, and Topology, Padua, 1997. Vol. 201 , Lecture Notes in Pure and Appl. Math. 261 – 278 . New York : Marcel Dekker, Inc. .
   Google Scholar
• Hajarnavis , C. R. and Norton , N. C. 1985 . On dual rings and their modules . J. Algebra , 93 : 253 – 266 . [CROSSREF]
   Google Scholar
• Herbera , D. and Shamsuddin , A. 1996 . On self-injective perfect rings . Canad. Math. Bull. , 39 ( 1 ) : 55 – 58 .
   Google Scholar
• Kasch , F. 1982 . Modules and Rings London, New York : Academic Press .
   Google Scholar
• Lam , T. Y. 1995 . Exercises in Classical Ring Theory, Problem Books in Mathematics Berlin-Heidelberg-New York : Springer-Verlag .
   Google Scholar
• Nicholson , W. K. and Yousif , M. F. 1995 . Principally injective rings . J. Algebra , 174 : 77 – 93 . [CROSSREF]
   Google Scholar
• Nicholson , W. K. and Yousif , M. F. 1997a . Mininjective rings . J. Algebra , 187 : 548 – 578 . [CROSSREF]
   Google Scholar
• Nicholson , W. K. and Yousif , M. F. 1997b . On perfect simple-injective rings . Proc. Amer. Math. Soc. , 125 ( 4 ) : 979 – 985 . [CROSSREF]
   Google Scholar
• Nicholson , W. K. and Yousif , M. F. 2001a . FP-rings . Comm. Algebra , 29 ( 1 ) : 415 – 425 . [CROSSREF]
   Google Scholar
• Nicholson , W. K. and Yousif , M. F. On Quasi-Frobenius rings . International Symposium on Ring Theory . June 28–July 3 1999 , South Korea . Edited by: Birkenmeier , G. F. , Park , J. K. and Park , Y. S. pp. 245 – 277 . Boston : Birkhäuser .
   Google Scholar
• Osofsky , B. L. 1966 . A generalization of quasi-Frobenius rings . J. Algebra , 4 : 373 – 388 . [CROSSREF]
   Google Scholar
• Rowen , L. H. 1988 . Ring Theory I New York : Academic Press .
   Google Scholar
• Rutter , E. A. Jr. 1975 . Rings with the principal extension property . Comm. Algebra , 3 ( 3 ) : 203 – 212 .
   Google Scholar
• Stenström , B. 1975 . Rings of Quotients Berlin, Heidelberg, New York : Springer-Verlag .
   Google Scholar
• Xue , W. 1996 . A note on perfect self-injective rings . Comm. Algebra , 24 ( 2 ) : 749 – 755 .
   Google Scholar
• #Communicated by S. Wiegand.
   Google Scholar