Amalgamating inverse semigroups over ample semigroups
We consider semigroup amalgams (S; T1, T2) in which T1 and T2 are inverse semigroups and S is a non-inverse semigroup. They are known to be non-embeddable if T1 and T2 are both groups (Clifford semigroups), but S is not such. We prove that (S; T1, T2) is non-embeddable if S is a non-inverse ample se...
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Estonian Academy Publishers
2025-01-01
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| Series: | Proceedings of the Estonian Academy of Sciences |
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| author | Nasir Sohail |
| author_facet | Nasir Sohail |
| author_sort | Nasir Sohail |
| collection | DOAJ |
| description | We consider semigroup amalgams (S; T1, T2) in which T1 and T2 are inverse semigroups and S is a non-inverse semigroup. They are known to be non-embeddable if T1 and T2 are both groups (Clifford semigroups), but S is not such. We prove that (S; T1, T2) is non-embeddable if S is a non-inverse ample semigroup. By introducing the notion of rich ampleness, we determine some necessary and sufficient conditions for the weak embedding of (S; T1, T2) in an inverse semigroup. In particular, (S; T1, T2) is shown to be weakly embeddable in a group if T1 and T2 are groups. A rudimentary analysis of the novel classes of rich ample semigroups is also provided. |
| format | Article |
| id | doaj-art-1bdbbb15a5a448eba79fa5cb9f09af8d |
| institution | Kabale University |
| issn | 1736-6046 1736-7530 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Estonian Academy Publishers |
| record_format | Article |
| series | Proceedings of the Estonian Academy of Sciences |
| spelling | doaj-art-1bdbbb15a5a448eba79fa5cb9f09af8d2025-02-10T10:10:04ZengEstonian Academy PublishersProceedings of the Estonian Academy of Sciences1736-60461736-75302025-01-017415061https://doi.org/10.3176/proc.2025.1.05https://doi.org/10.3176/proc.2025.1.05Amalgamating inverse semigroups over ample semigroupsNasir Sohail0Institute of Mathematics and Statistics, University of Tartu, 51009 Tartu, EstoniaWe consider semigroup amalgams (S; T1, T2) in which T1 and T2 are inverse semigroups and S is a non-inverse semigroup. They are known to be non-embeddable if T1 and T2 are both groups (Clifford semigroups), but S is not such. We prove that (S; T1, T2) is non-embeddable if S is a non-inverse ample semigroup. By introducing the notion of rich ampleness, we determine some necessary and sufficient conditions for the weak embedding of (S; T1, T2) in an inverse semigroup. In particular, (S; T1, T2) is shown to be weakly embeddable in a group if T1 and T2 are groups. A rudimentary analysis of the novel classes of rich ample semigroups is also provided.https://kirj.ee/wp-content/plugins/kirj/pub/proc-1-2025-50-61_20250128193135.pdfinverse semigroupamalgamantiamalgamation pairamplerich ample |
| spellingShingle | Nasir Sohail Amalgamating inverse semigroups over ample semigroups Proceedings of the Estonian Academy of Sciences inverse semigroup amalgam antiamalgamation pair ample rich ample |
| title | Amalgamating inverse semigroups over ample semigroups |
| title_full | Amalgamating inverse semigroups over ample semigroups |
| title_fullStr | Amalgamating inverse semigroups over ample semigroups |
| title_full_unstemmed | Amalgamating inverse semigroups over ample semigroups |
| title_short | Amalgamating inverse semigroups over ample semigroups |
| title_sort | amalgamating inverse semigroups over ample semigroups |
| topic | inverse semigroup amalgam antiamalgamation pair ample rich ample |
| url | https://kirj.ee/wp-content/plugins/kirj/pub/proc-1-2025-50-61_20250128193135.pdf |
| work_keys_str_mv | AT nasirsohail amalgamatinginversesemigroupsoveramplesemigroups |