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Proceedings of the American Mathematical Society

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

 

 

Two examples of local Artinian rings


Author: Wei Min Xue
Journal: Proc. Amer. Math. Soc. 107 (1989), 63-65
MSC: Primary 16A35; Secondary 16A52
DOI: https://doi.org/10.1090/S0002-9939-1989-0979222-2
MathSciNet review: 979222
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Abstract: We answer a question of D. A. Hill in the negative by providing two local artinian rings $ R$ and $ S$ such that $ R$ is right serial but the left indecomposable injective $ R$-module is not uniserial, and that $ S$ is not right serial but the left indecomposable injective $ S$-module is uniserial. Moreover $ R$ possesses a Morita duality but fails to have self-duality.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0979222-2
Keywords: Uniserial modules, serial rings, Morita duality
Article copyright: © Copyright 1989 American Mathematical Society