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Varieties satisfying the triangular scheme need not be congruence distributive

Ivan Chajda, Radomír Halaš (2007)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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...

Weak congruences of an algebra with the CEP and the WCIP

Andrzej Walendziak (2002)

Czechoslovak Mathematical Journal

Here we consider the weak congruence lattice C W ( A ) of an algebra A with the congruence extension property (the CEP for short) and the weak congruence intersection property (briefly the WCIP). In the first section we give necessary and sufficient conditions for the semimodularity of that lattice. In the second part we characterize algebras whose weak congruences form complemented lattices.

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