Congruence Pairs of Algebras Abstracting Double Kleene and Stone algebras

Leibo Wang

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Leibo Wang

Keywords:

double K_2-algebra, congruence pair, congruence permutable, congruence n-permutable

Abstract

In this note, we extend the result of Beazer on congruence pairs of $gif.latex?K_{2}$ -algebras to the class of double $gif.latex?K_{2}$ -algebras. We show that any congruence $gif.latex?\alpha$ on a double $gif.latex?K_{2}$ -algebra can be represented by a congruence pair $gif.latex?\left&space;\langle&space;\theta_{1},\theta_{2}&space;\right&space;\rangle$ , where $gif.latex?\theta_{1}$ is a Kleene congruence and $gif.latex?\theta_{2}$ is a lattice one. As an application of this result, we give a sufficient condition for a double $gif.latex?K_{2}$ -algebra is congruence permutable ( $gif.latex?n$ -permutable).

Congruence Pairs of Algebras Abstracting Double Kleene and Stone algebras

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