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,...