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Proceedings of the American Mathematical Society

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

 

 

Non-Artinian essential extensions of simple modules


Authors: K. R. Goodearl and A. H. Schofield
Journal: Proc. Amer. Math. Soc. 97 (1986), 233-236
MSC: Primary 16A33
MathSciNet review: 835871
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Abstract: A noetherian ring of Krull dimension one is constructed which possesses a simple module with a cyclic non-artinian essential extension. The construction also provides an example of a torsionfree noetherian bimodule which fails to satisfy Jategaonkar's density condition.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0835871-0
Keywords: Noetherian ring, simple module, essential extension
Article copyright: © Copyright 1986 American Mathematical Society