Perfect semigroups
John Fountain · Proceedings of the Edinburgh Mathematical Society · 1976
A semigroup S with identity is (left) perfect if every unitary left S-system has a projective cover. This is the semigroup analogue of the definition of left perfect rings introduced in (1). The investigation of perfect semigroups was initiated by Isbell (4), who proved that a semigroup is perfect if and only if it satisfies two conditions referred to as conditions A and D.