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A characterization of uniserial rings via continuous and discrete modules

Published online by Cambridge University Press:  09 April 2009

S. K. Jain ,
S. R. Lopez-Permouth  and
S. Tariq Rizvi
S. K. Jain
Affiliation:
Ohio University Athens, Ohio 45701, U.S.A.
S. R. Lopez-Permouth
Affiliation:
Ohio University Athens, Ohio 45701, U.S.A.
S. Tariq Rizvi
Affiliation:
Ohio University Lima, Ohio 45804, U.S.A.
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Abstract

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It is well-known that quasi-Frobenius rings are characterized by the property that all propective right modules are injective, as well as by the property that all injective right modules are projective. Similarly, either the property that every quasi-injective or that every quasi-injective is quasi-projective characterizes uniserial rings. Oshiro has given similar characterizations for generalized uniserial rings. The purpose of this paper is to characterize rings for which continuous right modules are discrete. We show that these rings are precisely the uniserial rings. The property that every discrete module is continuous is also investigated.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 2 , April 1991 , pp. 197 - 203
Copyright
Copyright © Australian Mathematical Society 1991

References

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