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 ${\mathcal{K}}_n$. As a consequence, we conclude that the identities of ${\mathcal{K}}_n$ are nonfinitely based for every $n\ge 4$ and exhibit a finite identity basis for the identities of each of the monoids ${\mathcal{K}}_2$ and ${\mathcal{K}}_3$. In the third version a question left open in the initial submission has beed answered.

16 pages, 1 table, 1 figure

References in corpus (3)

• On Kiselman quotients of 0-Hecke monoids
• Finitely based monoids
• Non-finitely based monoids

Cited by in corpus (2)

• Enumeration of idempotents in diagram semigroups and algebras
• Finitely based monoids