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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.06055 |
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| _version_ | 1866908634685898752 |
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| author | Barbina, Silvia Casanovas, Enrique |
| author_facet | Barbina, Silvia Casanovas, Enrique |
| contents | A free Steiner quasigroup is a free object in the variety of Steiner quasigroups. Free Steiner quasigroups are characterised by the existence of a levelled construction that starts with a free base - that is, a set of elements none of which is a product of the others, and which generate the quasigroup. Then each element in a free Steiner quasigroup $M$ can be obtained as a term on the free base. We characterise homomorphisms between substructures of a free Steiner quasigroup where one generator is replaced by a term in the original generators. The characterisation depends on certain synctactic properties of the term in question. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Endomorphisms of free Steiner quasigroups Barbina, Silvia Casanovas, Enrique Logic 03C05, 05B07 A free Steiner quasigroup is a free object in the variety of Steiner quasigroups. Free Steiner quasigroups are characterised by the existence of a levelled construction that starts with a free base - that is, a set of elements none of which is a product of the others, and which generate the quasigroup. Then each element in a free Steiner quasigroup $M$ can be obtained as a term on the free base. We characterise homomorphisms between substructures of a free Steiner quasigroup where one generator is replaced by a term in the original generators. The characterisation depends on certain synctactic properties of the term in question. |
| title | Endomorphisms of free Steiner quasigroups |
| topic | Logic 03C05, 05B07 |
| url | https://arxiv.org/abs/2412.06055 |