On φ-u-S-flat modules and nonnil-u-S-injective modules

Abstract

This paper introduces and studies the ϕ-u-S-flat (resp., nonnil-u-S-injective) modules, which are a generalization of both ϕ-flat modules and u-S-flat modules (resp., both nonnil-injective modules and u-S-injective modules). We give the Cartan–Eilenberg–Bass theorem for nonnil-u-S-Noetherian rings. Finally, we offer some new characterizations of the ϕ-von Neumann regular ring.