Distributive lattices with finite projective covers

Abstract

A projective cover in a category, J%, of algebras is a morphism \P-> A where A, Pe-%^, P is projective in Jf and no proper subalgebra of P has A as its direct image under . Projective covers of finite distributive lattices in the categories *?, of all lattices and -S^n of all finite lattices are determined (when they exist).