Geodesic
Varieties satisfying the triangular scheme need not be congruence distributive
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 46 (2007) no. 1, pp. 19-24 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A diagrammatic scheme characterizing congruence distributivity of congruence permutable algebras was introduced by the first author in 2001. It is known under the name Triangular Scheme. It is known that every congruence distributive algebra satisfies this scheme and an algebra satisfying the Triangular Scheme which is not congruence distributive was found by E. K. Horváth, G. Czédli and the autor in 2003. On the other hand, it was an open problem if a variety of algebras satisfying the Triangular Scheme must be congruence distributive. We get a negative solution by presenting an example.
A diagrammatic scheme characterizing congruence distributivity of congruence permutable algebras was introduced by the first author in 2001. It is known under the name Triangular Scheme. It is known that every congruence distributive algebra satisfies this scheme and an algebra satisfying the Triangular Scheme which is not congruence distributive was found by E. K. Horváth, G. Czédli and the autor in 2003. On the other hand, it was an open problem if a variety of algebras satisfying the Triangular Scheme must be congruence distributive. We get a negative solution by presenting an example.
Classification : 08A30, 08B05, 08B10
Keywords: congruence distributivity; Triangular Scheme; variety of algebras; Jónsson terms 
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Chajda, Ivan; Halaš, Radomír. Varieties satisfying the triangular scheme need not be congruence distributive. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 46 (2007) no. 1, pp. 19-24. http://geodesic.mathdoc.fr/item/AUPO_2007_46_1_a1/

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