Perfection for semigroups

Abstract

We call a semigroup right perfect if every object in the category of unitary right acts over that semigroup has a projective cover. In this paper, we generalize results about right perfect monoids to the case of semigroups. In our main theorem, we will give nine conditions equivalent to right perfectness of a factorizable semigroup. We also prove that right perfectness is a Morita invariant for factorizable semigroups.

Covers of Finitely Generated Acts over Monoids

“…Subsequently, several additional papers concerning covers have appeared (e.g., [7][8][9][10]). Recently, Irannezhad and Madanshekaf [11] researched covers of S-acts over monoids with Condition (P ′ ), and Qiao et al introduced Condition (PF ′′ ) covers in a similar way in [12].…”