Homomorphisms of distributive p-algebras with countably many minimal prime ideals
M. E. Adams, Vácłav Koubek, Jiří Sichler · Bulletin of the Australian Mathematical Society · 1987
According to a result of Lee, varieties of pseudocomplemented distributive lattices form an ω+1 chain in which is the trivial variety and is the variety of Boolean algebras. In the present paper it is shown that the variety contains an almost universal subcategory B in which the members of Hom(B,B') associated with minimal prime ideals of B form a countably infinite set for any B,B' ∈ B. In particular, B3contains arbitrarily large algebras whose nontrivial endomorphisms form the countably infinite right zero semigroup. Our earlier results concerning categorical properties of varieties of pseudocomplemented distributive lattices show that no further reduction of the right zero count is possible.