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

 

Modules with Artinian prime factors


Author: Efraim P. Armendariz
Journal: Proc. Amer. Math. Soc. 78 (1980), 311-314
MSC: Primary 16A30; Secondary 16A46, 16A64
MathSciNet review: 553364
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Abstract: An R-module M has Artinian prime factors if $ M/PM$ is an Artinian module for each prime ideal P of R. For commutative rings R it is shown that Noetherian modules with Artinian prime factors are Artinian. If R is either commutative or a von Neumann regular V-ring then the endomorphism ring of a module with Artinian prime factors is a strongly $ \pi $-regular ring.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0553364-X
PII: S 0002-9939(1980)0553364-X
Keywords: Artinian module, endomorphism ring, strongly $ \pi $-regular ring, von Neumann regular ring
Article copyright: © Copyright 1980 American Mathematical Society