Displaying similar documents to “A note on triangular schemes for weak congruences”

On schemes for congruence distributivity

I. Chajda, R. Halaš (2004)

Open Mathematics

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We present diagrammatic schemes characterizing congruence 3-permutable and distributive algebras. We show that a congruence 3-permutable algebra is congruence meetsemidistributive if and only if it is distributive. We characterize varieties of algebras satisfying the so-called triangular scheme by means of a Maltsev-type condition.

Varieties satisfying the triangular scheme need not be congruence distributive

Ivan Chajda, Radomír Halaš (2007)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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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...

Subalgebras and homomorphic images of algebras having the CEP and the WCIP

Andrzej Walendziak (2004)

Czechoslovak Mathematical Journal

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In the present paper we consider algebras satisfying both the congruence extension property (briefly the CEP) and the weak congruence intersection property (WCIP for short). We prove that subalgebras of such algebras have these properties. We deduce that a lattice has the CEP and the WCIP if and only if it is a two-element chain. We also show that the class of all congruence modular algebras with the WCIP is closed under the formation of homomorphic images.

Semiregularity of congruences implies congruence modularity at 0

Ivan Chajda (2002)

Czechoslovak Mathematical Journal

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We introduce a weakened form of regularity, the so called semiregularity, and we show that if every diagonal subalgebra of 𝒜 × 𝒜 is semiregular then 𝒜 is congruence modular at 0.