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// Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports]
// Archive
Sib. Èlektron. Mat. Izv.,
2015
Volume 12,
Pages
818–831
(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
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.
UDC:
512.567
MSC:
06B15
Received
July 13, 2015
, published
November 14, 2015
DOI:
10.17377/semi.2015.12.068
Fulltext:
PDF file (191 kB)
References
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Steklov Math. Inst. of RAS
, 2024