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Continuous Rings with Acc on Annihilators

Published online by Cambridge University Press:  20 November 2018

Victor Camillo  and
Mohamed F. Yousif
Victor Camillo
Affiliation:
Department of Mathematics, Ohio State University, Lima Campus, 4240 Campus Drive, Lima, Ohio, USA 45804
Mohamed F. Yousif
Affiliation:
University of Iowa, Iowa City, Iowa, USA 55242
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Abstract

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It is shown that a two-sided continuous ring with ascending chain condition on left annihilators is quasi-Frobenius.

Keywords

16A3616A3416A5216A35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 4 , 01 December 1991 , pp. 462 - 464
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Armendariz, E. P., Rings with dec on essential left ideals, Comm. in Alg. 8 (1980), 299–308.Google Scholar
2. Dung, N. V., D. v. Huynh and Wisbauer, R., Quasi-injective modules with ace or dec on essential submodules, Arch. Math. 53 (1989), 252–255.Google Scholar
3. Faith, C., Rings with ascending chain condition on annihilators, Nagoya Math. J. 27 (1966), 179–191.Google Scholar
4. Jain, S. K., S. R. Lopez-Permouth and Rizvi, S. T., Continuous rings with ace on essentials are artinian, Proc. Amer. Math. Soc. 108 (1990), 583–586.Google Scholar
5. Miiller, B. J. and Rizvi, S. T., On injective and quasi-continuous modules, J. Pure and App. Alg. 28 (1983), 197–210.Google Scholar
6. Okado, M., On the decomposition of extending modules, Math. Japonica 29 (1984), 939–941.Google Scholar
7. Stenstrom, B., Rings of quotients. Springer-Verlag, New York-Heidelberg-Berlin, 1975.Google Scholar
8. Utumi, Y., On continuous rings and self-injective rings, Trans. Amer. Math. Soc. 118 (1965), 158–173.Google Scholar