On congruence distributivity of ordered algebras with constants

Abstract

We define the order-congruence distributivity at 0 and ordercongruence n-distributivity at 0 of ordered algebras with a nullary operation 0. These notions are generalizations of congruence distributivity and congruence n-distributivity. We prove that a class of ordered algebras with a nullary operation 0 closed under taking subalgebras and direct products is order-congruence distributive at 0 iff it is ordercongruence n-distributive at 0. We also characterize such classes by a Mal'tsev condition.