The Finite Basis Problem for Kiselman Monoids

The Finite Basis Problem for Kiselman Monoids

In an earlier paper, the second-named author has described the identities holding in the so-called Catalan monoids. Here we extend this description to a certain family of Hecke-Kiselman monoids including the Kiselman monoids Kn. As a consequence, we conclude that the identities of Kn are nonfinitely...

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Main Authors: Ashikhmin D. N., Volkov M. V., Zhang Wen Ting
Format: Article
Language:English
Published: De Gruyter 2015-12-01
Series:Demonstratio Mathematica
Subjects:
Kiselman monoids
Catalan monoids
Hecke-Kiselman monoids
semigroup identity
equational theory
finite basis problem
Online Access:http://www.degruyter.com/view/j/dema.2015.48.issue-4/dema-2015-0035/dema-2015-0035.xml?format=INT
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spelling doaj-d4062cbc0fa64511998e54e1f06e716e2020-11-25T01:11:33ZengDe GruyterDemonstratio Mathematica0420-12132391-46612015-12-0148447549210.1515/dema-2015-0035dema-2015-0035The Finite Basis Problem for Kiselman MonoidsAshikhmin D. N.0Volkov M. V.1Zhang Wen Ting2Institute of Mathematics and Computer Science Ural Federal University, Lenina 51, 620000 Ekaterinburg, RussiaInstitute of Mathematics and Computer Science Ural Federal University, Lenina 51, 620000 Ekaterinburg, RussiaSchool of Mathematics and Statistics Lanzhou University, Lanzhou, Gansu 730000, ChinaIn an earlier paper, the second-named author has described the identities holding in the so-called Catalan monoids. Here we extend this description to a certain family of Hecke-Kiselman monoids including the Kiselman monoids Kn. As a consequence, we conclude that the identities of Kn are nonfinitely based for every n ≥4 and exhibit a finite identity basis for the identities of each of the monoids K2 and K3.http://www.degruyter.com/view/j/dema.2015.48.issue-4/dema-2015-0035/dema-2015-0035.xml?format=INTKiselman monoidsCatalan monoidsHecke-Kiselman monoidssemigroup identityequational theoryfinite basis problem
collection DOAJ
language English
format Article
sources DOAJ
author Ashikhmin D. N.
Volkov M. V.
Zhang Wen Ting
spellingShingle Ashikhmin D. N.
Volkov M. V.
Zhang Wen Ting
The Finite Basis Problem for Kiselman Monoids
Demonstratio Mathematica
Kiselman monoids
Catalan monoids
Hecke-Kiselman monoids
semigroup identity
equational theory
finite basis problem
author_facet Ashikhmin D. N.
Volkov M. V.
Zhang Wen Ting
author_sort Ashikhmin D. N.
title The Finite Basis Problem for Kiselman Monoids
title_short The Finite Basis Problem for Kiselman Monoids
title_full The Finite Basis Problem for Kiselman Monoids
title_fullStr The Finite Basis Problem for Kiselman Monoids
title_full_unstemmed The Finite Basis Problem for Kiselman Monoids
title_sort finite basis problem for kiselman monoids
publisher De Gruyter
series Demonstratio Mathematica
issn 0420-1213
2391-4661
publishDate 2015-12-01
description In an earlier paper, the second-named author has described the identities holding in the so-called Catalan monoids. Here we extend this description to a certain family of Hecke-Kiselman monoids including the Kiselman monoids Kn. As a consequence, we conclude that the identities of Kn are nonfinitely based for every n ≥4 and exhibit a finite identity basis for the identities of each of the monoids K2 and K3.
topic Kiselman monoids
Catalan monoids
Hecke-Kiselman monoids
semigroup identity
equational theory
finite basis problem
url http://www.degruyter.com/view/j/dema.2015.48.issue-4/dema-2015-0035/dema-2015-0035.xml?format=INT
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