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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
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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.


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Keywords: Test module, <IMG WIDTH="20" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\Sigma$">-module, direct sums of modules, co-generator, simple module, essential extension, injective hull
Article copyright: © Copyright 1975 American Mathematical Society