Ockham Algebras with Balanced Double Pseudocomplementation

摘要

In this paper, we introduce a variety bdO of Ockham algebras with balanced double pseudocomplementation, consisting of those algebras (L; Ù, Ú, f, *,+, 0, 1){(L; wedge, vee, f,,^{*},^{+}, 0, 1)} of type á2, 2, 1, 1, 1, 0, 0ñ{langle2,,2,,1,,1,,1,,0,,0rangle} where (L; Ù, Ú, f, 0, 1){(L; wedge, vee, f, 0, 1)} is an Ockham algebra, (L; Ù, Ú, f, *,+, 0, 1){(L; wedge, vee, f,,^{*},^{+}, 0, 1)} is a double p-algebra, and the operations x ® f(x), x ® x*{x mapsto f(x), x mapsto x^{*}} and x ® x+{x mapsto x^{+}} are linked by the identities [f(x)]* = [f(x)]+ = f 2(x), f(x*) = x ** and f(x +) = x ++. We give a description of the congruences on the algebras, and show that there are precisely nine non-isomorphic subdirectly irreducible members in the class of the algebras via the Priestley duality. We also describe all axioms in the variety bdO, and provide a characterization of all subvarieties of bdO determined by 12 none-equivalent axioms, identifying therein the biggest subvariety in which every principal congruence is complemented.