On T-Noncosingular Modules

Abstract

In this paper we introduce T-noncosingular modules. Rings for which all right modules are T-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.