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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Projective modules
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by S. Jøndrup PDF
Proc. Amer. Math. Soc. 59 (1976), 217-221 Request permission

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
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 59 (1976), 217-221
  • MSC: Primary 16A50
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0419525-4
  • MathSciNet review: 0419525