The importance of rational extensions

Frans Loonstra

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1988)

  • Volume: 82, Issue: 4, page 623-628
  • ISSN: 1120-6330

Abstract

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The rational completion M ¯ of an R -module M can be characterized as a τ M -injective hull of M with respect to a (hereditary) torsion functor τ M depending on M . Properties of a torsion functor depending on an R -module M are studied.

How to cite

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Loonstra, Frans. "The importance of rational extensions." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.4 (1988): 623-628. <http://eudml.org/doc/287457>.

@article{Loonstra1988,
abstract = {The rational completion $\bar\{M\}$ of an $R$-module $M$ can be characterized as a $\tau_\{M\}$-injective hull of $M$ with respect to a (hereditary) torsion functor $\tau_\{M\}$ depending on $M$. Properties of a torsion functor depending on an $R$-module $M$ are studied.},
author = {Loonstra, Frans},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Torsion-functor; Rational extension; rational extensions; rational completion; injective hull; torsion functor},
language = {eng},
month = {12},
number = {4},
pages = {623-628},
publisher = {Accademia Nazionale dei Lincei},
title = {The importance of rational extensions},
url = {http://eudml.org/doc/287457},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Loonstra, Frans
TI - The importance of rational extensions
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/12//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 4
SP - 623
EP - 628
AB - The rational completion $\bar{M}$ of an $R$-module $M$ can be characterized as a $\tau_{M}$-injective hull of $M$ with respect to a (hereditary) torsion functor $\tau_{M}$ depending on $M$. Properties of a torsion functor depending on an $R$-module $M$ are studied.
LA - eng
KW - Torsion-functor; Rational extension; rational extensions; rational completion; injective hull; torsion functor
UR - http://eudml.org/doc/287457
ER -

References

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  1. GOODEARL, K.R. (1976) - Ring theory, p. 56. MR429962
  2. GOLAN, J.S. (1975) - Localization of non-comm. rings, p. 24. 
  3. GOLDMAN, O. (1969) - Rings and modules of quotients, J. of Algebra, 13, 1969, 10-47. Zbl0201.04002MR245608

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