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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Test modules
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by T. Cheatham and R. Cumbie PDF
Proc. Amer. Math. Soc. 49 (1975), 311-314 Request permission

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
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  • Tom Head, Preservation of coproducts by $\textrm {Hom}_R(M,-)$, Rocky Mountain J. Math. 2 (1972), no. 2, 235–237. MR 294388, DOI 10.1216/RMJ-1972-2-2-235
    • R. Rentschler, Die Vertauschbarkeit des Hom-functor mit directen Summen, Docktoral These, University München, Munich, 1967. —, Sur les modules $M$ tels que $\operatorname {Hom} (M, - )$ commute avec les sommes directes, C. R. Acad. Sci. Paris Ser. A-B 268 (1969), A930-A933. MR 39 #2806.
  • A. K. Tiwary, On the quotients of indecomposable injective modules, Canad. Math. Bull. 9 (1966), 187–190. MR 204451, DOI 10.4153/CMB-1966-024-1
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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