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One Sided SF-Rings with Certain Chain Conditions

Published online by Cambridge University Press:  20 November 2018

Yufei Xiao*
Affiliation:
Department of Mathematics, University of Iowa Iowa City, Iowa 52242 U.S.A.
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Abstract

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We prove that with some weak chain conditions, left SF-rings are semisimple Artinian or regular. We also prove that MERT left SF-rings are really regular.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Anderson, F. W. and Fuller, K. R., Rings and categories of modules, Springer-Verlag, 1974.Google Scholar
2. Baccella, G., Von Neumann regularity of V-rings with Artinian primitive factor rings, Proc. Amer. Math. Soc. (3) 103(1988), 747749.Google Scholar
3. Fuller, K. R., Artinian rings, Murcia, Universidad, Secretariado de Publicaciones, 1989.Google Scholar
4. Goodearl, K. R., Ring theory, Nonsingular rings and modules, 1976.Google Scholar
5. Goodearl, K. R., Von Neumann regular rings, Pitman, London-San Francisco-Melbourne, 1979.Google Scholar
6. Goodearl, K. R., Singular torsion and the splitting properties, Mem. Amer. Math. Soc. 124, (1972).Google Scholar
7. Goursaud, J. M. and Valette, J., Sur l'enveloppe injective des anneaux de groupes régulier, Bull.Soc. Math. France 103(1975), 91102.Google Scholar
8. Kertesz, A., Vorlesungen iiber artinsche ringe, Budapest, 1968.Google Scholar
9. Ming, Y. C., On biregularity and regularity, Comm. Algebra (3) 20(1992), 749759.Google Scholar
10. Ramamurthi, V. S., On the injectivity and flatness of certain cyclic modules, Proc. Amer. Math.Soc. 48(1975), 2125.Google Scholar
11. Rege, M. K., On Von Neumann regular rings and SF-rings, Math. Japon. 31(1986), 927936.Google Scholar
12. Zhang, Z. and Du, X., Von Neumann regularity of SF-rings, Comm. Algebra, to appear.Google Scholar