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ON 𝒯-NONCOSINGULAR MODULES

Part of: Modules, bimodules and ideals

Published online by Cambridge University Press:  02 July 2009

DERYA KESKIN TÜTÜNCÜ  and
RACHID TRIBAK
DERYA KESKIN TÜTÜNCÜ*
Affiliation:
Department of Mathematics, Hacettepe University, 06800 Beytepe, Ankara, Turkey (email: keskin@hacettepe.edu.tr)
RACHID TRIBAK
Affiliation:
Département de Mathématiques, Faculté des Sciences de Tétouan, B.P. 21.21, Tétouan, Morocco (email: tribak12@yahoo.com)
*
✉For correspondence; e-mail: keskin@hacettepe.edu.tr
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Abstract

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In this paper we introduce 𝒯-noncosingular modules. Rings for which all right modules are𝒯-noncosingular are shown to be precisely those for which every simple right module is injective. Moreover, for any ring R we show that the right R-module R is 𝒯-noncosingular precisely when R has zero Jacobson radical. We also study the 𝒯-noncosingular condition in association with (strongly) FI-lifting modules.

Keywords

𝒯-noncosingular module(strongly) FI-lifting module

MSC classification

Secondary: 16D10: General module theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 80 , Issue 3 , December 2009 , pp. 462 - 471
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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