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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| Format: | Article |
| Language: | English |
| Published: |
Estonian Academy Publishers
2025-01-01
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| Series: | Proceedings of the Estonian Academy of Sciences |
| Subjects: | |
| Online Access: | https://kirj.ee/wp-content/plugins/kirj/pub/proc-1-2025-50-61_20250128193135.pdf |
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| Summary: | 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. |
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| ISSN: | 1736-6046 1736-7530 |