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On Pseudo-Frobenius Rings

Published online by Cambridge University Press:  20 November 2018

Mohamed F. Yousif ,
Yiqiang Zhou  and
Nasr Zeyada
Mohamed F. Yousif
Affiliation:
Department of Mathematics, Ohio State University, Lima, OH 45804, U.S.A., andThe American University in Cairo, Egypt e-mail: [email protected]
Yiqiang Zhou
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St.John’s, Newfoundland, A1C 5S7 e-mail: [email protected]
Nasr Zeyada
Affiliation:
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
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Abstract

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It is proved here that a ring $R$ is right pseudo-Frobenius if and only if $R$ is a right Kasch ring such that the second right singular ideal is injective.

Keywords

16D5016L60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 2 , 01 June 2005 , pp. 317 - 320
Copyright
Copyright © Canadian Mathematical Society 2005

References

[1] Faith, C., Algebra, II. Ring Theory. Grundlehren der Mathematischen Wissenschaften 191, Springer-Verlag, Berlin, 1976.Google Scholar
[2] García Hernández, J. L. and Gómez Pardo, J. L., Closed submodules of free modules over the endomorphism ring of a quasi-injective module. Comm. Algebra 16(1988), 115–137.Google Scholar
[3] Gómez Pardo, J. L. and Asensio, P. A. Guil, Torsionless modules and rings with finite essential socle. In: Abelian groups, module theory, and topology, Lecture Notes in Pure and Appl. Math. 201, Dekker, New York, 1998, pp. 261–278,Google Scholar
[4] Mohamed, S. H. and Müller, B. J., Continuous and Discrete Modules. London Mathematical Society Lecture Note Series 147, Cambridge University Press, Cambridge, 1990.Google Scholar
[5] Nicholson, W. K. and Yousif, M. F., Quasi-Frobenius Rings. Cambridge Tracts in Mathematics 158, Cambridge University Press, Cambridge, 2003.Google Scholar
[6] Osofsky, B., A generalization of quasi-Frobenius rings. J. Algebra 4(1966), 373–387.Google Scholar
[7] Yousif, M. F., On continuous rings. J. Algebra 191(1997), 495–509.Google Scholar
[8] Yousif, M. F. and Zhou, Y., Pseudo-Frobenius rings: characterizations and questions. Comm. Algebra 31(2003), 4473–4484.Google Scholar
[9] Yue Chi Ming, R., On p-injectivity, Y J-injectivity and quasi-Frobeniusean rings. Comment.Math. Univ. Carolinae 43(2002), 33–42.Google Scholar
[10] Zhou, Y., Rings in which certain right ideals are direct summands of annihilators. J. Aust. Math. Soc. 73(2002), 335–346.Google Scholar