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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the derived quotient module


Author: C. N. Winton
Journal: Trans. Amer. Math. Soc. 154 (1971), 315-321
MSC: Primary 16.40
DOI: https://doi.org/10.1090/S0002-9947-1971-0276268-8
MathSciNet review: 0276268
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Abstract: With every R-module M associate the direct limit of $ {\operatorname{Hom}_R}(D,M)$ over the dense right ideals of R, the derived quotient module $ \mathcal{D}(M)$ of M. $ \mathcal{D}(M)$ is a module over the complete ring of right quotients of R. Relationships between $ \mathcal{D}(M)$ and the torsion theory of Gentile-Jans are explored and functorial properties of $ \mathcal{D}$ are discussed. When M is torsion free, results are given concerning rational closure, rational completion, and injectivity.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0276268-8
Keywords: Derived quotient module, complete ring of right quotients, dense right ideal, left perfect ring, torsion free module, rational closure, rational completion, torsion submodule, minimal dense right ideal
Article copyright: © Copyright 1971 American Mathematical Society