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

This article is cited in 1 scientific paper (total 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.

Full text: PDF file (140 kB)
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UDC: 512.532.2
Received: 09.02.2012

Citation: V. Yu. Shaprynskii, “The periodicity of special elements in the lattice of semigroup varieties”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 3, 2012, 282–286

Citation in format AMSBIB
\Bibitem{Sha12}
\by V.~Yu.~Shaprynskii
\paper The periodicity of special elements in the lattice of semigroup varieties
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 3
\pages 282--286
\mathnet{http://mi.mathnet.ru/timm861}
\elib{http://elibrary.ru/item.asp?id=17937033}


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    This publication is cited in the following articles:
    1. S. V. Gusev, “On the lattice of overcommutative varieties of monoids”, Russian Math. (Iz. VUZ), 62:5 (2018), 23–26  mathnet  crossref  isi
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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