Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 175–186
Mathematical logic, algebra and number theory
On modular and cancellable elements of the lattice of semigroup varieties
D. V. Skokov, B. M. Vernikov
Ural Federal University, Institute of Natural Sciences and Mathematics,
51, Lenina str.,
Ekaterinburg, 620000, Russia
We continue a study of modular and cancellable elements in the lattice SEM of all semigroup varieties. In 2007, the second author completely determined all commutative semigroup varieties that are modular elements in SEM. In 2018 the authors jointly with S.V.Gusev proved that, within the class of commutative varieties, the properties to be modular and cancellable elements in SEM are equivalent. The objective of this article is to verify that, within some slightly wider class of semigroup varieties, this equivalence is not the case. To achieve this goal, we completely classify semigroup varieties satisfying a permutational identity of length 3 that are modular elements in SEM. Further, we specify a variety with these properties that is not a cancellable element in SEM.
semigroup, variety, lattice of varieties, permutational identity, modular element of a lattice, cancellable element of a lattice.
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Received March 26, 2018, published February 6, 2019
D. V. Skokov, B. M. Vernikov, “On modular and cancellable elements of the lattice of semigroup varieties”, Sib. Èlektron. Mat. Izv., 16 (2019), 175–186
Citation in format AMSBIB
\by D.~V.~Skokov, B.~M.~Vernikov
\paper On modular and cancellable elements of the lattice of semigroup varieties
\jour Sib. \`Elektron. Mat. Izv.
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