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Artinian right serial rings

Author: Surjeet Singh
Journal: Proc. Amer. Math. Soc. 125 (1997), 2239-2240
MSC (1991): Primary 16P20; Secondary 16D50
MathSciNet review: 1377006
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Abstract: Let $R$ be an artinian ring such that for the Jacobson radical $J$ of $R$, $R/J$ is a direct product of matrix rings over finite-dimensional division rings. Then the following are proved to be equivalent: (1) Every indecomposable injective left $R$-module is uniserial. (2) $R$ is right serial.

References [Enhancements On Off] (What's this?)

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  • 2. K. R. Fuller, On indecomposable injectives over artinian rings, Pacific J. Math. 29 (1969), 115-135. MR 40:186
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  • 4. D. A. Hill, Rings whose indecomposable injective modules are uniserial, Canad. J. Math. 34 (1982), 797-805. MR 84h:16016
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Additional Information

Surjeet Singh
Affiliation: Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Received by editor(s): December 14, 1995
Received by editor(s) in revised form: February 22, 1996
Additional Notes: This research was partially supported by the Kuwait University Research Grant No. SM126.
Communicated by: Ken Goodearl
Article copyright: © Copyright 1997 American Mathematical Society

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