Almost-Perfect Rings and Modules

Author: Amini Babak   Amini Afshin   Ershad Majid  

Publisher: Taylor & Francis Ltd

ISSN: 0092-7872

Source: Communications in Algebra, Vol.37, Iss.12, 2009-12, pp. : 4227-4240

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Abstract

Following [1], a ring R is called right almost-perfect if every flat right R-module is projective relative to R. In this article, we continue the study of these rings and will find some new characterizations of them in terms of decompositions of flat modules. Also we show that a ring R is right almost-perfect if and only if every right ideal of R is a cotorsion module. Furthermore, we prove that over a right almost-perfect ring, every flat module with superfluous radical is projective. Moreover, we define almost-perfect modules and investigate some properties of them.