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arXiv · 2405.19825

E-disjunctive inverse semigroups

Luna Elliott·Alex Levine·James Mitchell
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Abstract

In this paper we provide an overview of the class of inverse semigroups $S$ such that every congruence on $S$ relates at least one idempotent to a non-idempotent; such inverse semigroups are called $E$-disjunctive. This overview includes the study of the inverse semigroup theoretic structure of $E$-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 $E$-disjunctive.

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Luna Elliott, Alex Levine, James Mitchell. 2024-05-30. E-disjunctive inverse semigroups. https://doi.org/10.1016/j.jalgebra.2025.08.041

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