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Izv. Vyssh. Uchebn. Zaved. Mat., 2011, Number 7, Pages 13–21 (Mi ivm7693)  

This article is cited in 4 scientific papers (total in 4 papers)

Codistributive elements of the lattice of semigroup varieties

B. M. Vernikov

Chair of Algebra and Discrete Mathematics, Ural State University, Ekaterinburg, Russia

Abstract: We prove that if a semigroup variety is a codistributive element of the lattice SEM of all semigroup varieties then it either coincides with the variety of all semigroups or is a variety of semigroups with completely regular square. We completely classify strongly permutative varieties that are codistributive elements of SEM. We prove that a semigroup variety is a costandard element of the lattice SEM if and only if it is a neutral element of this lattice. In view of results obtained earlier, this gives a complete description of costandard elements of the lattice SEM.

Keywords: semigroup, variety, lattice, codistributive element, costandard element, neutral element.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:7, 9–16

Bibliographic databases:

UDC: 512.532
Received: 14.04.2010

Citation: B. M. Vernikov, “Codistributive elements of the lattice of semigroup varieties”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 7, 13–21; Russian Math. (Iz. VUZ), 55:7 (2011), 9–16

Citation in format AMSBIB
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\by B.~M.~Vernikov
\paper Codistributive elements of the lattice of semigroup varieties
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 7
\pages 13--21
\mathnet{http://mi.mathnet.ru/ivm7693}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2931712}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 7
\pages 9--16
\crossref{https://doi.org/10.3103/S1066369X11070024}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051682734}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Yu. Shaprynskii, “Periodichnost spetsialnykh elementov reshetki mnogoobrazii polugrupp”, Tr. IMM UrO RAN, 18, no. 3, 2012, 282–286  mathnet  elib
    2. D. V. Skokov, “Spetsialnye elementy nekotorykh tipov v reshetke mnogoobrazii epigrupp”, Tr. IMM UrO RAN, 22, no. 3, 2016, 244–250  mathnet  crossref  mathscinet  elib
    3. Vernikov B.M., “Upper-Modular and Related Elements of the Lattice of Commutative Semigroup Varieties”, Semigr. Forum, 94:3 (2017), 696–711  crossref  mathscinet  zmath  isi  scopus
    4. Gusev S.V., “Special Elements of the Lattice of Monoid Varieties”, Algebr. Universalis, 79:2 (2018), UNSP 29  crossref  mathscinet  isi  scopus
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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