Rings which have (m,n)-flat injective modules

Abstract

A ring R is said to be a left IF − (m, n) ring if every injective left R-module is (m, n)-flat. In this paper, several characterizations of left IF − (m, n) rings are investigated, some conditions under which R is left IF−(m, n) are given. Furthermore, conditions under which a left IF −1 ring (i.e., IF −(1, 1) ring) is a field, a regular ring and a semisimple ring are studied respectively.