Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A64

Retrieve articles in all journals with MSC: 16A64


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