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Proceedings of the American Mathematical Society

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Test modules


Authors: T. Cheatham and R. Cumbie
Journal: Proc. Amer. Math. Soc. 49 (1975), 311-314
MSC: Primary 16A64
DOI: https://doi.org/10.1090/S0002-9939-1975-0371958-X
MathSciNet review: 0371958
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Abstract: The results of this paper arose from an investigation of the class of $ \Sigma $-modules, i.e. those modules $ M$ for which $ {\operatorname{Hom} _R}(M, - )$ commutes with direct sums. A module $ T$ is called a test module if $ {\operatorname{Hom} _R}(M, - )$ commutes with direct sums of copies of $ T$ only when $ M$ is a $ \Sigma $-module. Test modules are characterized and their relation to cogenerators is investigated.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0371958-X
Keywords: Test module, $ \Sigma $-module, direct sums of modules, co-generator, simple module, essential extension, injective hull
Article copyright: © Copyright 1975 American Mathematical Society

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