The Adherence Order on Renner-Coxeter Monoids

TL;DR

This paper introduces the Adherence order on Renner-Coxeter monoids, explores its relation to Green's relations, and studies extremal elements within equivalence classes, extending prior algebraic structures.

Contribution

It defines the Adherence order on Renner-Coxeter monoids and analyzes its properties in relation to Green's relations, including extremal elements in finite cases.

Findings

Defined the Adherence order on Renner-Coxeter monoids

Analyzed Green's relations in relation to the Adherence order

Identified maximum and minimum elements in finite equivalence classes

Abstract

Building upon the previous Renner-Coxeter system of work by Eddy Godelle we introduce the familiar Renner monoid structure of the Adherence order. The Green's relations of the system are then considered in relation to the Adherence order and in the finite case maximum and minimum elements in each equivalence class are distinguished and studied.