Complemented congruences on double Ockham algebras

Abstract

For $n ∈ \mathbb{N}$ and $m ∈ \mathbb{N}_0$, an algebra $L = (L, ∧, ∨, f, g, 0, 1)$ of type $(2, 2, 1, 1, 0, 0)$ is said to be a double $K_{n,m}$-algebra, if L is a double Ockham algebra that satisfies the identities $f^{2n+m} = f^m, g^{2n+m} = g^m, fg = g^{2zn} and gf = f^{2zn}, where z is the smallest natural number greater than or equal to m/2n. In this papaer we describe the complement (when it exists) of a principal congruence and, using this description, we also determine when the complement exists.