On the derived quotient module
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- by C. N. Winton
- Trans. Amer. Math. Soc. 154 (1971), 315-321
- DOI: https://doi.org/10.1090/S0002-9947-1971-0276268-8
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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.References
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Bibliographic Information
- © Copyright 1971 American Mathematical Society
- 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