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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Bibliographic Details
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
Description
Summary: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.
ISSN:0420-1213
2391-4661

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