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
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.
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 Inst. Mat. i Mekh. UrO RAN, 18, no. 3, 2012, 282–286
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\paper The periodicity of special elements in the lattice of semigroup varieties
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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