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Proceedings of the American Mathematical Society

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

 

 

Regular $ P.I.$-rings


Authors: E. P. Armendariz and Joe W. Fisher
Journal: Proc. Amer. Math. Soc. 39 (1973), 247-251
MSC: Primary 16A38; Secondary 16A30
DOI: https://doi.org/10.1090/S0002-9939-1973-0313305-3
MathSciNet review: 0313305
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Abstract: For a ring $ R$ which satisfies a polynomial identity we show that the following are equivalent: (1) $ R$ is von Neumann regular, (2) each two-sided ideal of $ R$ is idempotent, and (3) each simple left (right) $ R$-module is injective. We show that a P.I.-ring $ R$ is left perfect if and only if all left $ R$-modules have maximal submodules and $ R$ has no infinite sets of orthogonal idempotents.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0313305-3
Keywords: von Neumann regular, $ V$-rings, polynomial identity, simple modules injective, completely reducible modules injective, idempotent rings, modules containing maximal submodules, perfect ring
Article copyright: © Copyright 1973 American Mathematical Society