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Artinian right serial rings

Author(s): Surjeet Singh
Journal: Proc. Amer. Math. Soc. 125 (1997), 2239-2240.
MSC (1991): Primary 16P20; Secondary 16D50
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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:

1.: F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer Verlag, 1974. MR 54:5281
2.: K. R. Fuller, On indecomposable injectives over artinian rings, Pacific J. Math. 29 (1969), 115-135. MR 40:186
3.: I. N. Herstein, Non-commutative Rings, The Carus Monograph Number 15, The Mathematical Association of America, 1968. MR 37:2790
4.: D. A. Hill, Rings whose indecomposable injective modules are uniserial, Canad. J. Math. 34 (1982), 797-805. MR 84h:16016
5.: Weimin Xue, Two examples of local artinian rings, Proc. Amer. Math. Soc. 107 (1989), 63-65. MR 90d:16017

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Additional Information:

Surjeet Singh
Affiliation: Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Email: singh@math-1.sci.kuniv.edu.kw

DOI: 10.1090/S0002-9939-97-03820-3
PII: S 0002-9939(97)03820-3
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
Copyright of article: Copyright 1997, American Mathematical Society


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