Diameters of endomorphism monoids of chains

Autor:	East, James, Gould, Victoria, Miller, Craig, Quinn-Gregson, Thomas
Rok vydání:	2024
Předmět:	Mathematics - Rings and Algebras Mathematics - Combinatorics
Druh dokumentu:	Working Paper
Popis:	The left and right diameters of a monoid are topological invariants defined in terms of suprema of lengths of derivation sequences with respect to finite generating sets for the universal left or right congruences. We compute these parameters for the endomorphism monoid $End(C)$ of a chain $C$. Specifically, if $C$ is infinite then the left diameter of $End(C)$ is 2, while the right diameter is either 2 or 3, with the latter equal to 2 precisely when $C$ is a quotient of $C{\setminus}\{z\}$ for some endpoint $z$. If $C$ is finite then so is $End(C),$ in which case the left and right diameters are 1 (if $C$ is non-trivial) or 0. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.00416 Zobrazit plný text záznamu View this record from Arxiv