The Finite Basis Problem for Kiselman Monoids

2014/11/02 by D. N. Ashikhmin, Mikhail V. Volkov, Ashikhmin, D. N. +3 · 1 citation
Arts and Humanities · Computer Science · Mathematics · #20M07 20M05 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Historical Linguistics and Language Studies #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1411.0223

openalex publication_date 2014/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 K_n. As a consequence, we conclude that the identities of K_n are nonfinitely based for every n≥ 4 and exhibit a finite identity basis for the identities of each of the monoids K₂ and K₃. In the third version a question left open in the initial submission has beed answered.

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• A complete classification of endomorphisms of Kiselman's semigroup

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