On the Homological Classification of Semigroups with Local Units

Abstract

In this paper, we study homological classification of semigroups with local units depending on properties around projectivity and flatness of acts over them, the results form a new progress in this research area. First, we show that Hom functors and tensor functors in the category of acts over semigroups are left and right exact, respectively. Then we characterize semigroups with local units over which all acts have some property with respect to (principal) weak flatness and torsion freeness of acts. Finally, we establish relationships between several different properties and Rees short exact sequence of acts.