Complemented congruences on double Ockham algebras

• Autor(a) principal: Mendes, C.
• Data de Publicação: 2007
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/11551
• topic: Double Ockham algebras; Congruences; Distributive lattices; Ockham algebras; Double algebras; Science & Technology

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.