J Austral Math Soc Ser A 50 pp197--203, 1991.

A Characterization of Uniserial Rings Via Continuous and Discrete Modules

S. K. Jain, S. R. Lopez-Permouth and S. Tariq Rizvi

(Received 22 March 1989; revised 24 August 1989)

Abstract

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 every quasi-projective is 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.

1980 AMS Subject Classification (1985 Revision): 16A35, 16A36, 16A50, 16A51, 16A52

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Authors

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

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Last Modified: Mon Feb 3 9:46:09 2003