E-disjunctive inverse semigroups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917914228031488 |
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| author | Elliott, Luna Levine, Alex Mitchell, James |
| author_facet | Elliott, Luna Levine, Alex Mitchell, James |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | E-disjunctive inverse semigroups Elliott, Luna Levine, Alex Mitchell, James Group Theory 20M18 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. |
| title | E-disjunctive inverse semigroups |
| topic | Group Theory 20M18 |
| url | https://arxiv.org/abs/2405.19825 |