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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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).


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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