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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2012 Volume 18, Number 3, Pages 282–286 (Mi timm861)

This article is cited in 1 paper

The periodicity of special elements in the lattice of semigroup varieties

V. Yu. Shaprynskii

Ural Federal University

Abstract: The notion of $I$-element of a lattice is introduced, where $I$ is an arbitrary lattice identity. This notion generalizes practically all types of special elements of lattices considered earlier. It is proved that, if a semigroup variety is an $I$-element of the lattice of all semigroup varieties for some nontrivial lattice identity $I$ and is different from the variety of all semigroups, then it is a periodic variety. It is established that the converse is not true.

Keywords: semigroup, variety, lattice of varieties, special elements of a lattice.

UDC: 512.532.2

Received: 09.02.2012



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