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 | References | Similar Articles | Additional Information
Abstract: With every R-module M associate the direct limit of over the dense right ideals of R, the derived quotient module
of M.
is a module over the complete ring of right quotients of R. Relationships between
and the torsion theory of Gentile-Jans are explored and functorial properties of
are discussed. When M is torsion free, results are given concerning rational closure, rational completion, and injectivity.
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Additional Information
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