Test modules and cogenerators
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- by Peter Vámos PDF
- Proc. Amer. Math. Soc. 56 (1976), 8-10 Request permission
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
- T. Cheatham and R. Cumbie, Test modules, Proc. Amer. Math. Soc. 49 (1975), 311–314. MR 371958, DOI 10.1090/S0002-9939-1975-0371958-X
- D. W. Sharpe and P. Vámos, Injective modules, Cambridge Tracts in Mathematics and Mathematical Physics, No. 62, Cambridge University Press, London-New York, 1972. MR 0360706
- P. Vámos, A note on the quotients of indecomposable injective modules, Canad. Math. Bull. 12 (1969), 661–665. MR 255529, DOI 10.4153/CMB-1969-085-3
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 8-10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0399178-4
- MathSciNet review: 0399178