Relational depth of transformation semigroups and their ideals
Group Theory
2026-04-06 v1
Abstract
We introduce the concept of relational depth of a finite semigroup whose -classes form a chain. It captures how far down in the ideal structure one is obliged to go in order to define the semigroup by generators and defining relations. We determine the exact value for the relational depth of an arbitrary ideal in the full transformation monoid, symmetric inverse monoid and in the partial transformation monoid.
Keywords
Cite
@article{arxiv.2604.02495,
title = {Relational depth of transformation semigroups and their ideals},
author = {N. Ruškuc and Z. Yayi},
journal= {arXiv preprint arXiv:2604.02495},
year = {2026}
}