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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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Rings whose right modules are direct sums of indecomposable modules
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by Birge Zimmermann-Huisgen PDF
Proc. Amer. Math. Soc. 77 (1979), 191-197 Request permission

Abstract:

It is shown that, given a module M over a ring with 1, every direct product of copies of M is a direct sum of modules with local endomorphism rings if and only if every direct sum of copies of M is algebraically compact. As a consequence, the rings whose right modules are direct sums of indecomposable modules coincide with those whose right modules are direct sums of finitely generated modules.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 77 (1979), 191-197
  • MSC: Primary 16A64
  • DOI: https://doi.org/10.1090/S0002-9939-1979-0542083-3
  • MathSciNet review: 542083