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MC2 RINGS AND WQD RINGS*

Published online by Cambridge University Press:  01 September 2009

JUNCHAO WEI  and
LIBIN LI
JUNCHAO WEI
Affiliation:
School of Mathematics, Yangzhou University, Yangzhou 225002, P. R. China E-mail: [email protected]
LIBIN LI
Affiliation:
School of Mathematics, Yangzhou University, Yangzhou 225002, P. R. China E-mail: [email protected]
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Abstract

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We introduce in this paper the concepts of rings characterized by minimal one-sided ideals and concern ourselves with rings containing an injective maximal left ideal. Some known results for idempotent reflexive rings and left HI rings can be extended to left MC2 rings. As applications, we are able to give some new characterizations of regular left self-injective rings with non-zero socle and extend some known results for strongly regular rings.

Keywords

16A3016A5016E5016D30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 3 , September 2009 , pp. 691 - 702
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Chen, W. X., On semiabelian π-regular rings, Intern. J. Math. Sci. 23 (2007), 1–10.CrossRefGoogle Scholar
2.Kaplansky, I., Rings of operators (W. A. Benjamin, New York, 1968).Google Scholar
3.Kim, J. Y., Certain rings whose simple singular modules are GP-injective, Proc. Japan. Acad. 81 (2005), 125–128.Google Scholar
4.Kim, J. Y. and Baik, J. U., On idempotent reflexive rings, Kyungpook Math. J. 46 (2006), 597–601.Google Scholar
5.Kim, N. K., Nam, S. B. and Kim, J. Y., On simple singular GP–injective modules, Comm. Algebra 27 (5) (1999), 2087–2096.CrossRefGoogle Scholar
6.Lam, T. Y. and Dugas, A. S., Quasi-duo rings and stable range descent, J. Pure Appl. Algebra 195 (2005), 243–259.CrossRefGoogle Scholar
7.Mason, G., Reflexive ideals, Comm. Algebra 9 (17) (1981), 1709–1724.CrossRefGoogle Scholar
8.Ming, R. Y. C., On regular rings and self-injective rings, ∏, Glasnik Mat. 18 (38) (1983), 25–32.Google Scholar
9.Nicholson, W. K. and Watters, J. F., Rings with projective socle, Proc. Amer. Math. Soc. 102 (1988), 443–450.CrossRefGoogle Scholar
10.Nicholson, W. K. and Yousif, M. F., Principally injective rings, J. Algebra 174 (1995), 77–93.CrossRefGoogle Scholar
11.Nicholson, W. K. and Yousif, M. F., Minijective rings, J. Algebra 187 (1997), 548–578.CrossRefGoogle Scholar
12.Nicholson, W. K. and Yousif, M. F., Weakly continuous and C2-rings, Comm. Algebra 29 (6) (2001), 2429–2466.CrossRefGoogle Scholar
13.Osofsky, B. L., Rings all of whose finitely generated modules are injective, Pacific J. Math. 14 (1964), 645–650.CrossRefGoogle Scholar
14.Rege, M. B., On von Neumann regular rings and SF rings, Math Japonica 31 (1986), 927–936.Google Scholar
15.Song, X. M. and Yin, X. B., Generalizations of V-rings, Kyungpook Math. J. 45 (2005), 357–362.Google Scholar
16.Wei, J. C., The rings characterized by minimal left ideal, Acta. Math. Sinica. Engl. Ser. 21 (3) (2005), 473–482.CrossRefGoogle Scholar
17.Wei, J. C., On simple singular YJ-injective modules, Southeast Asian Bull. Math. 31 (2007), 1009–1018.Google Scholar
18.Wei, J. C. and Chen, J. H., nil-injective rings, Int. Electron. J. Algebra 2 (2007), 1–21.Google Scholar
19.Yousif, M. F., On continuous rings, J. Algebra 191 (1997), 495–509.CrossRefGoogle Scholar
20.Yu, H. P., On quasi-duo rings, Glasgow Math. J. 37 (1995), 21–31.CrossRefGoogle Scholar
21.Zhang, J. L. and Du, X. N., Hereditary rings containing an injective maximal left ideal, Comm. Algebra 21 (1993), 4473–4479.Google Scholar