Some Properties of Grey S-Acts Over Monoids

Abstract

In this paper, we introduce the concept of grey S-acts and morphisms between grey S-acts on monoids, which construct a category, namely, [Formula: see text]. Next, we define indecomposable, cyclic, free and projective grey S-acts. We show that any grey S-act is a free grey S-act if and only if it is a free object in this category. Also, we show that any grey S-act is epimorphism image of any free grey S-act. We prove that any free grey S-act is a projective grey S-act and any cyclic grey S-act is an indecomposable grey S-act.