Geodesic
The periodicity of special elements in the lattice of semigroup varieties
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 282-286 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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V. Yu. Shaprynskii. The periodicity of special elements in the lattice of semigroup varieties. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 282-286. http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a30/

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