Ideals and finiteness conditions for subsemigroups

TL;DR

This paper investigates how certain finiteness conditions related to ideal structures in semigroups are preserved when considering subsemigroups or supersemigroups with finite Rees or Green index, focusing on properties like stability and minimal ideal conditions.

Contribution

It introduces new results on the preservation of ideal-related finiteness conditions in semigroups with finite Rees or Green index, expanding understanding of their structural properties.

Findings

Finiteness conditions are preserved under finite Rees index subsemigroups.

Stability and D=J conditions are analyzed for preservation in sub- and supersemigroups.

Minimal ideal conditions are shown to be maintained under certain finiteness assumptions.

Abstract

In this paper we consider a number of finiteness conditions for semigroups related to their ideal structure, and ask whether such conditions are preserved by sub- or supersemigroups with finite Rees or Green index. Specific properties under consideration include stability, D=J and minimal conditions on ideals.