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Proceedings of the American Mathematical Society

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



Test modules and cogenerators

Author: Peter Vámos
Journal: Proc. Amer. Math. Soc. 56 (1976), 8-10
MathSciNet review: 0399178
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Abstract | References | Additional Information

Abstract: If $ {\operatorname{Hom} _R}(A,T) = 0$ implies that $ A = 0$ for all $ R$-modules $ A$, then the $ R$-module $ T$ is a test module. The ring $ R$ is said to be a TC-ring if every test module is a cogenerator. If $ S$ is a simple module over a TC-ring then $ {\operatorname{End} _R}E(S)$ is a local semifir. A commutative ring $ R$ is a TC-ring if and only if $ {R_M}$ is a P.I.D. for all maximal ideals $ M$ of $ R$.

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

  • [1] T. Cheatham and R. Cumbie, Test modules, Proc. Amer. Math. Soc. 49 (1975), 311-314. MR 0371958 (51:8175)
  • [2] D. W. Sharpe and P. Vámos, Injective modules, Cambridge Univ. Press, New York, 1972. MR 0360706 (50:13153)
  • [3] P. Vámos, A note on the quotients of indecomposable injective modules, Canad. Math. Bull. 12 (1969), 661-665. MR 41 #190. MR 0255529 (41:190)

Additional Information

Keywords: Test module, cogenerator, indecomposable injective, endomorphism ring, semifir, P.I.D
Article copyright: © Copyright 1976 American Mathematical Society

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