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Fundam. Prikl. Mat., 2008, Volume 14, Issue 7, Pages 43–51 (Mi fpm1172)  

This article is cited in 6 scientific papers (total in 6 papers)

Upper-modular elements of the lattice of semigroup varieties. II

B. M. Vernikov

Ural State University

Abstract: A semigroup variety is called a variety of degree $\le2$ if all its nilsemigroups are semigroups with zero multiplication, and a variety of degree $>2$ otherwise. We completely determine all semigroup varieties of degree $>2$ that are upper-modular elements of the lattice of all semigroup varieties and find quite a strong necessary condition for semigroup varieties of degree $\le2$ to have the same property.

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English version:
Journal of Mathematical Sciences (New York), 2010, 164:2, 182–187

Bibliographic databases:

UDC: 512.532

Citation: B. M. Vernikov, “Upper-modular elements of the lattice of semigroup varieties. II”, Fundam. Prikl. Mat., 14:7 (2008), 43–51; J. Math. Sci., 164:2 (2010), 182–187

Citation in format AMSBIB
\Bibitem{Ver08}
\by B.~M.~Vernikov
\paper Upper-modular elements of the lattice of semigroup varieties.~II
\jour Fundam. Prikl. Mat.
\yr 2008
\vol 14
\issue 7
\pages 43--51
\mathnet{http://mi.mathnet.ru/fpm1172}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2533596}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 164
\issue 2
\pages 182--187
\crossref{https://doi.org/10.1007/s10958-009-9718-2}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-71649103279}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. M. Vernikov, V. Yu. Shaprynskii, “Distributive elements of the lattice of semigroup varieties”, Algebra and Logic, 49:3 (2010), 201–220  mathnet  crossref  mathscinet  zmath
    2. B. M. Vernikov, “Codistributive elements of the lattice of semigroup varieties”, Russian Math. (Iz. VUZ), 55:7 (2011), 9–16  mathnet  crossref  mathscinet
    3. Shaprynskii V.Yu., Vernikov B.M., “Special elements in the lattice of overcommutative semigroup varieties revisited”, Order, 28:1 (2011), 139–155  crossref  mathscinet  zmath  isi  elib
    4. A. G. Gein, M. P. Shushpanov, “Finitely generated lattices with completely modular elements among generators”, Algebra and Logic, 52:6 (2014), 435–441  mathnet  crossref  mathscinet  isi
    5. 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
    6. Gusev S.V., “Special Elements of the Lattice of Monoid Varieties”, Algebr. Universalis, 79:2 (2018), UNSP 29  crossref  mathscinet  isi  scopus
  • Фундаментальная и прикладная математика
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