Perfektsed poolrühmad

"Perfect ring" is a classical notion in ring theory. A ring with identity is called right perfect if all unitary right modules over it have a projective cover. "Projective cover" is a purely category theoretical notion.

Perfect monoids were first studied by John Isbell and John Fountain, who wrote two fundamental articles on this topic. Later, several other mathematicians (including Mati Kilp and Victoria Gould) have studied perfect monoids. Our aim is to generalize the most important results about perfect monoids to the case of perfect semigroups.

We call a semigroup S right perfect if every unitary right S-act has a projective cover. We show that for factorisable semigroups, right perfectness is a Morita invariant. As a consequence, we obtain an example of a class of (right) perfect semigroups.