Strongly Max-Flat Modules

Abstract

Let R be a ring. A left R-module M is called strongly max-flat if for every simple right R-module S and every i ≥ 1. In this article, we show that the class of strongly max-flat R-modules and its Ext-orthogonal class form a perfect and hereditary cotorsion pair. This result has some applications to the characterizations of right SF, semisimple, left perfect, von Neumann regular and quasi-Frobenius rings.