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/

[1] G. Birkhoff, On the structure of abstract algebras, Proc. Cambridge Phil. Soc. 31 (1935), 433-454. doi: 10.1017/S0305004100013463

[2] S.L. Bloom, Varieties of ordered algebras, J. Comput. System Sci. 13 (1976), 200-212. doi: 10.1016/S0022-0000(76)80030-X

[3] I. Chajda, Congruence distributivity in varieties with constants, Arch. Math. (Brno) 22 (1986), 121-124.

[4] G. Czédli, On the lattice of congruence varieties of locally equational classes, Acta Sci. Math. (Szeged) 41 (1979), 39-45.

[5] G. Czédli, Notes on congruence implication, Archivum Math. (Brno) 27 (1991), 149-153.

[6] G. Czédli and E.K. Horváth, All congruence lattice identities implying modularity have Mal'tsev conditions, Algebra Universalis 50 (2003), 69-74. doi: 10.1007/s00012-003-1818-0

[7] G. Czédli, E.K. Horváth, P. Lipparini, Optimal Mal'tsev conditions for congruence modular varieties, Algebra Universalis 53 (2005), 267-279. doi: 10.1007/s00012-005-1893-5

[8] G. Czédli and A. Lenkehegyi, On congruence n-distributivity of ordered algebras, Acta Math. (Hung.) 41 (1983), 17-26. doi: 10.1007/BF01994057

[9] R. Freese and B. Jónsson, Congruence modularity implies the Arguesian identity, Algebra Universalis 6 (2) (1976), 225-228. doi: 10.1007/BF02485830

[10] R. Freese and R. McKenzie, Commutator theory for congruence modular varieties, London Mathematical Society Lecture Note Series, 125, Cambridge University Press, Cambridge 1987.

[11] G. Grätzer, Universal Algebra, Springer-Verlag (Berlin-Heidelberg-New York 1979).

[12] C. Herrmann and A.P. Huhn, Lattices of normal subgroups which are generated by frames, Lattice Theory, Colloq. Math. Soc. J. Bolyai, North-Holland 14 (1976), 97-136.

[13] A.P. Huhn, Schwach distributive Verbände I, Acta Sci. Math. (Szeged) 33 (1972), 297-305.

[14] A.P. Huhn, Two notes on n-distributive lattices, Lattice Theory, Colloq. Math. Soc. J. Bolyai, North-Holland 14 (1976), 137-147.

[15] A.P. Huhn, n-distributivity and some questions of the equational theory of lattices, Contributions to Universal Algebra, Colloq. Math. Soc. J. Bolyai North-Holland 17 (1977), 177-178.

[16] B. Jónsson, Congruence varieties, Algebra Universalis 10 (1980), 355-394. doi: 10.1007/BF02482916

[17] J.B. Nation, Varieties whose congruences satisfy certain lattice identities, Algebra Univ. 4 (1974), 78-88.