Endomorphism monoids of distributive double p-algebras

Abstract

A distributive p-algebra is an algebra 〈L; ∨, ∧, *, 0, 1〉 for which 〈L, ∨, ∧, 0, 1〉 is a bounded distributive lattice and * is a unary operation on L such that a ∧ x = 0 if and only if x ≤ a* (i.e. a pseudocomplementation). A distributive double p-algebra is an algebra 〈L; ∨, ∧, *, +, 0, 1〉 in which the deletion of + gives a distributive p-algebra and the deletion of * gives a dual distributive p-algebra, that is a ∨ (x = 1 if and only if x ≥ a+.