The Finite Basis Problem for Kiselman Monoids

Abstract

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.

Keywords

• Kiselman monoids
• Catalan monoids
• Hecke-Kiselman monoids
• semigroup identity
• equational theory
• finite basis problem