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On modular elements of the lattice of semigroup varieties

Boris M. Vernikov — 2007

Commentationes Mathematicae Universitatis Carolinae

A semigroup variety is called if it is a modular element of the lattice of all semigroup varieties. We obtain a strong necessary condition for a semigroup variety to be modular. In particular, we prove that every modular nil-variety may be given by 0-reduced identities and substitutive identities only. (An identity u = v is called if the words u and v depend on the same letters and v may be obtained from u by renaming of letters.) We completely determine all commutative modular varieties and obtain...

On congruences of G -sets

Boris M. Vernikov — 1997

Commentationes Mathematicae Universitatis Carolinae

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 .

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