E-disjunctive inverse semigroups

Elliott, Luna, Levine, Alex and Mitchell, James (2026) E-disjunctive inverse semigroups. Journal of Algebra, 687. pp. 292-344. ISSN 0021-8693

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Abstract

In this paper we provide an overview of the class of inverse semigroups S such that every non-trivial 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.

Item Type:	Article
Additional Information:	Data availability statement: No data was used for the research described in the article. Funding information: The second named author was supported by a London Mathematical Society Early Career Fellowship (ECF-2022-09) and the Heilbronn Institute for Mathematical Research during this work.
Uncontrolled Keywords:	e-disjunctive,idempotent-pure,inverse semigroup,algebra and number theory ,/dk/atira/pure/subjectarea/asjc/2600/2602
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	18 Sep 2025 09:32
Last Modified:	11 Oct 2025 15:33
URI:	https://ueaeprints.uea.ac.uk/id/eprint/100435
DOI:	10.1016/j.jalgebra.2025.08.041

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