Ockham Algebras With Balanced Double Demi-Pseudocomplementation

摘要

The variety bddpO of Ockham algebras with balanced double demi- pseudocomplementation consists of those algebras (L; ∧, ∨, f,* ,+ , 0,1) of type 〈2, 2, 1, 1, 1, 0, 0〉 where (L;f) is an Ockham algebra, (L; ∧, ∨,*,0,1) is a double demi-p-lattice and the operations x → f (x), x → x~* and x → x~+ are linked by the identities [f(x)]~* = [f(x)]~+ = f~2(x), f(x~*) = x~(**) and f(x~+) = x~(++) . In this paper, we discuss the properties of the congruences on bddpO-algebras, and give a description of the structure of the lattice congruences of a subdirectly irreducible bddpOalgebra.