On Covers of Acts over Semigroups

Abstract

Let S be a monoid and X a class of S-acts which is closed under coproducts. The object of this article is to find conditions under which all S-acts have X-precovering. We have shown that the existence of torsion-free precovering implies the existence of torsion-free covering. This work is an attempt to further facilitate the study of the conjecture that all S-acts have flat cover.