Modules with ADS-(pre)envelopes and ADS-(pro)covers

Abstract

This paper focusses on the question of when modules have ADS- preenvelopes and covers. For a ring R, it is proved that every ADS module over R is injective if and only if every right R-module has an ADS-(pre)envelope (an ADS-(pre)cover). In this paper, we also introduce a generalization of ADS modules stated in terms of their invariance under certain automorphisms of their envelopes.