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
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

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