E-disjunctive inverse semigroups
Group Theory
2025-02-07 v2
Abstract
In this paper we provide an overview of the class of inverse semigroups such that every congruence on relates at least one idempotent to a non-idempotent; such inverse semigroups are called -disjunctive. This overview includes the study of the inverse semigroup theoretic structure of -disjunctive semigroups; a large number of natural examples; some asymptotic results establishing the rarity of such inverse semigroups; and a general structure theorem for all inverse semigroups where the building blocks are -disjunctive.
Cite
@article{arxiv.2405.19825,
title = {E-disjunctive inverse semigroups},
author = {Luna Elliott and Alex Levine and James Mitchell},
journal= {arXiv preprint arXiv:2405.19825},
year = {2025}
}
Comments
38 pages, 3 figures, 1 table (updated to account for referee's comments, and to fix other minor issues)