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

 

Projective modules


Author: S. Jøndrup
Journal: Proc. Amer. Math. Soc. 59 (1976), 217-221
MSC: Primary 16A50
MathSciNet review: 0419525
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Abstract: In this note we prove that if $ R$ is a ring satisfying a polynomial identity and $ P$ is a projective left $ R$-module such that $ P$ is finitely generated modulo the Jacobson radical, then $ P$ is finitely generated. As a corollary we get that if $ R$ is a ring still satisfying a polynomial identity and $ M$ is a finitely generated flat $ R$-module such that $ M/JM$ is $ R/J$-projective, then $ M$ is $ R$-projective, $ J$ denotes the Jacobson radical.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0419525-4
PII: S 0002-9939(1976)0419525-4
Keywords: Flat and projective module, Nakayama lemma and P.I. ring
Article copyright: © Copyright 1976 American Mathematical Society