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Proceedings of the American Mathematical Society

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

 
 

 

Rings whose right modules are direct sums of indecomposable modules


Author: Birge Zimmermann-Huisgen
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1979-0542083-3
Keywords: Indecomposable module, ring of finite representation type, exchange property, cancellation property
Article copyright: © Copyright 1979 American Mathematical Society

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