Rings whose right modules are direct sums of indecomposable modules

Zimmermann-Huisgen, Birge

doi:10.1090/S0002-9939-1979-0542083-3

Rings whose right modules are direct sums of indecomposable modules
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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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