Geodesic
On congruence distributivity of ordered algebras with constants
Discussiones Mathematicae. General Algebra and Applications, Tome 31 (2011) no. 1, pp. 47-59

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We define the order-congruence distributivity at 0 and order- congruence 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 order-congruence n-distributive at 0. We also characterize such classes by a Mal'tsev condition.
Keywords: ordered algebra, n-distributivity, distributivity, Mal'tsev condition 
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Balog, Krisztina; Skublics, Benedek. On congruence distributivity of ordered algebras with constants. Discussiones Mathematicae. General Algebra and Applications, Tome 31 (2011) no. 1, pp. 47-59. http://geodesic.mathdoc.fr/item/DMGAA_2011_31_1_a2/