Displaying similar documents to “Congruence lattices of intransitive G-Sets and flat M-Sets”

On congruences of G -sets

Boris M. Vernikov (1997)

Commentationes Mathematicae Universitatis Carolinae

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We describe G -sets whose congruences satisfy some natural lattice or multiplicative restrictions. In particular, we determine G -sets with distributive, arguesian, modular, upper or lower semimodular congruence lattice as well as congruence n -permutable G -sets for n = 2 , 2 . 5 , 3 .

A visual approach to test lattices

Gábor Czédli (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Let p be a k -ary lattice term. A k -pointed lattice L = ( L ; ∨ , ∧ , d 1 , ... , d k ) will be called a p -lattice (or a test lattice if p is not specified), if ( L ; ∨ , ∧ ) is generated by { d 1 , ... , d k } and, in addition, for any k -ary lattice term q satisfying p ( d 1 , ... , d k ) ≤ q ( d 1 , ... , d k ) in L , the lattice identity p ≤ q holds in all lattices. In an elementary visual way, we construct a finite p -lattice L ( p ) for each p . If p is a canonical lattice term, then L ( p ) coincides with the optimal p -lattice of Freese, Ježek and Nation [Freese,...

Weak congruences of an algebra with the CEP and the WCIP

Andrzej Walendziak (2002)

Czechoslovak Mathematical Journal

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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.

Join-closed and meet-closed subsets in complete lattices

František Machala, Vladimír Slezák (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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To every subset A of a complete lattice L we assign subsets J ( A ) , M ( A ) and define join-closed and meet-closed sets in L . Some properties of such sets are proved. Join- and meet-closed sets in power-set lattices are characterized. The connections about join-independent (meet-independent) and join-closed (meet-closed) subsets are also presented in this paper.