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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Essential extensions and intersection theorems


Author: W. Schelter
Journal: Proc. Amer. Math. Soc. 53 (1975), 328-330
MSC: Primary 16A46
MathSciNet review: 0389971
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Abstract: If $ R$ is right and left noetherian, primitive factor rings are artinian, and $ R$ is right fully bounded, then a simple proof is given to show that finitely generated essential extensions of right artinian modules are artinian. An immediate corollary is that $ \cap _{n = 1}^\infty {J^n} = 0$ for such a ring.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0389971-5
PII: S 0002-9939(1975)0389971-5
Article copyright: © Copyright 1975 American Mathematical Society