A complete classification of endomorphisms of Kiselman’s semigroup

Andrenšek, Luka (author)

Kiselman’s semigroup $K_n$ was studied by Kudryavtseva and Mazorchuk, who posed the question of whether it is possible to classify all endomorphisms of $K_n$. In this paper, we provide a complete classification of endomorphisms of $K_n$ and present a Boolean matrix monoid that is isomorphic to $\operatorname{End}(K_n)$.

• Language: English
• Keywords: Kiselman’s semigroup, endomorphisms, monoids, semigroups
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: Str. 706-715
• Numbering: Vol. 112, iss. 3
• PID: 20.500.12556/RUL-183245
• UDC: 512
• ISSN on article: 0037-1912
• DOI: 10.1007/s00233-025-10577-4
• COBISS.SI-ID: 250252547
• Publication date in RUL: 09.06.2026

Record is a part of a journal

• Title: Semigroup forum
• Publisher: Springer Nature
• ISSN: 0037-1912
• COBISS.SI-ID: 26378752

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: Kiselmanova polgrupa, endomorfizmi, monoidi, polgrupe