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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2015, Volume 12, Pages 818–831
DOI: https://doi.org/10.17377/semi.2015.12.068 (Mi semr631) 		 
Mathematical logic, algebra and number theory

Representation of distributive algebraic spatial lattices by congruence lattices of semigroups and groupoids

A. L. Popovich

Ural Federal University, pr. Lenina, 51, 620083, Ekaterinburg, Russia
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DOI: https://doi.org/10.17377/semi.2015.12.068
Abstract: We prove that every distributive algebraic spatial lattice is isomorphic to the congruence lattice of some semigroup and also of some groupoid with zero satisfying identities $x^2=0$ and $xy=yx$.
Keywords: congruence lattice, semigroup, groupoid, spatial lattice.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 2248
НШ-5161.2014.1
Russian Foundation for Basic Research 14-01-00524_а
Received July 13, 2015, published November 14, 2015
Document Type: Article
UDC: 512.567
MSC: 06B15
Language: Russian
Citation: A. L. Popovich, “Representation of distributive algebraic spatial lattices by congruence lattices of semigroups and groupoids”, Sib. Èlektron. Mat. Izv., 12 (2015), 818–831
Citation in format AMSBIB
\Bibitem{Pop15}
\by A.~L.~Popovich
\paper Representation of distributive algebraic spatial lattices by congruence lattices of semigroups and groupoids
\jour Sib. \`Elektron. Mat. Izv.
\yr 2015
\vol 12
\pages 818--831
\mathnet{http://mi.mathnet.ru/semr631}
\crossref{https://doi.org/10.17377/semi.2015.12.068}
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