Projective distributive p-algebras
Alasdair Urquhart · Bulletin of the Australian Mathematical Society · 1981
A characterization of finite (weak) projectives in an equational class of distributive pseudocomplemented lattices is given. In the class of all such lattices, a finite lattice is projective if and only if its poset of join–irreducible elements forms a semilattice in which the minimal elements below the join of x and y are exactly the mininal elements below x or y. A similar condition works for any equational subclass.