Congruences on balanced pseudocomplemented Ockham algebras

Abstract

The variety bpO consists of those algebras (L; ∧, ∨, f,*) of type 〈2, 2, 1, 1, 0, 0〉 where (L; ∧, ∨, f, 0, 1) is an Ockham algebra, (L; ∧, ∨, *, 0, 1) is a p-algebra, and the operations x ↦ f(x) and x ↦ x* satisfy the identities f(x*) = x** and [f(x)]* = f 2(x). In this note, we show that the compact congruences on a bpO-algebra form a dual Stone lattice. Using this, we characterize the algebras in which every principal congruence is complemented. We also give a description of congruence coherent bpO-algebras.