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 and cogenerators


Author: Peter Vámos
Journal: Proc. Amer. Math. Soc. 56 (1976), 8-10
DOI: https://doi.org/10.1090/S0002-9939-1976-0399178-4
MathSciNet review: 0399178
Full-text PDF Free Access

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?)


Additional Information

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