n-IFP-flat modules and n-IFP-injective modules

Abstract

In this paper, we introduce the concept of [Formula: see text]-flat (respectively, [Formula: see text]-[Formula: see text]-injective) modules as nontrivial generalization of flat (respectively, injective) modules. We first investigate various properties of these modules. For example, we show that over any ring [Formula: see text], every [Formula: see text]-module has an [Formula: see text]-preenvelope, where [Formula: see text] is class of all [Formula: see text]-[Formula: see text]-flat right [Formula: see text]-modules. Secondly, we investigate the existence of [Formula: see text]-[Formula: see text]-injective covers. It is shown that over any ring [Formula: see text], [Formula: see text]-[Formula: see text]-injective cover always exists. Finally, we show that [Formula: see text] is a perfect cotorsion theory.