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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2015-12-01
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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 |
work_keys_str_mv |
AT ashikhmindn thefinitebasisproblemforkiselmanmonoids AT volkovmv thefinitebasisproblemforkiselmanmonoids AT zhangwenting thefinitebasisproblemforkiselmanmonoids AT ashikhmindn finitebasisproblemforkiselmanmonoids AT volkovmv finitebasisproblemforkiselmanmonoids AT zhangwenting finitebasisproblemforkiselmanmonoids |
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