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Algebra Discrete Math., 2018, Volume 26, Issue 1, Pages 34–46 (Mi adm668)  

This article is cited in 1 scientific paper (total in 1 paper)

RESEARCH ARTICLE

Cancellable elements of the lattice of semigroup varieties

Sergey V. Gusev, Dmitry V. Skokov, Boris M. Vernikov

Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia

Abstract: We completely determine all commutative semigroup varieties that are cancellable elements of the lattice SEM of all semigroup varieties. In particular, we verify that a commutative semigroup variety is a cancellable element of the lattice SEM if and only if it is a modular element of this lattice.

Keywords: semigroup, variety, cancellable element of a lattice, modular element of a lattice.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00551
Ministry of Science and Higher Education of the Russian Federation 1.6018.2017
The work is partially supported by Russian Foundation for Basic Research (grant 17-01-00551) and by the Ministry of Education and Science of the Russian Federation (project 1.6018.2017).


Full text: PDF file (351 kB)
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MSC: Primary 20M07; Secondary 08B15
Received: 30.03.2017
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Citation: Sergey V. Gusev, Dmitry V. Skokov, Boris M. Vernikov, “Cancellable elements of the lattice of semigroup varieties”, Algebra Discrete Math., 26:1 (2018), 34–46

Citation in format AMSBIB
\Bibitem{GusSkoVer18}
\by Sergey~V.~Gusev, Dmitry~V.~Skokov, Boris~M.~Vernikov
\paper Cancellable elements of the lattice of~semigroup~varieties
\jour Algebra Discrete Math.
\yr 2018
\vol 26
\issue 1
\pages 34--46
\mathnet{http://mi.mathnet.ru/adm668}


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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. D. V. Skokov, B. M. Vernikov, “On modular and cancellable elements of the lattice of semigroup varieties”, Sib. elektron. matem. izv., 16 (2019), 175–186  mathnet  crossref
  • Algebra and Discrete Mathematics
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