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A generalization of the Wedderburn-Artin theorem


Authors: S. K. Jain and S. R. López-Permouth
Journal: Proc. Amer. Math. Soc. 106 (1989), 19-23
MSC: Primary 16A36; Secondary 16A48
DOI: https://doi.org/10.1090/S0002-9939-1989-0948153-6
MathSciNet review: 948153
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Abstract: The structure of rings such that each of its homomorphic images has the property that each cyclic right module over it is essentially embeddable in a direct summand is determined. Such rings are precisely (i) right uniserial rings, (ii) $ n \times n$ matrix rings over two-sided uniserial rings with $ n > 1$, or (iii) sums of rings of the types (i) and (ii).


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

  • [1] F. W. Anderson and Kent R. Fuller, Rings and categories of modules, Springer-Verlag, Berlin, Heidelberg and New York, 1974. MR 0417223 (54:5281)
  • [2] H. Bass, Finitistic dimension and a homological generalization of semiprimary rings, Trans. Amer. Math. Soc. 95 (1960), 466-488. MR 0157984 (28:1212)
  • [3] C. Faith, Algebra: Rings, modules and categories. II, Springer-Verlag, Berlin, Heidelberg and New York, 1976. MR 0366960 (51:3206)
  • [4] V. K. Goel and S. K. Jain, $ \pi $-Injective modules and rings whose cyclics are $ \pi $-injective, Comm. Algebra 6 (1978), 59-73. MR 0491819 (58:11016)
  • [5] B. L. Osofsky, Noncommutative rings whose cyclic modules have cyclic injective hulls, Pacific J. Math. 25 (1978), 331-340. MR 0231858 (38:186)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0948153-6
Keywords: Essential submodules, right uniserial rings, self-injective rings
Article copyright: © Copyright 1989 American Mathematical Society

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