$F$-inverse monoids as algebraic structures in enriched signature
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| Acceso en línea: | |
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| _version_ | 1866910690359377920 |
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| author | Auinger, K. Kudryavtseva, G. Szendrei, M. B. |
| author_facet | Auinger, K. Kudryavtseva, G. Szendrei, M. B. |
| contents | Every $F$-inverse monoid can be equipped with the unary operation which maps each element to the maximum element of its $σ$-class. In this enriched signature, the class of all $F$-inverse monoids forms a variety of algebraic structures. We describe universal objects in several classes of $F$-inverse monoids, in particular free $F$-inverse monoids. More precisely, for every $X$-generated group $G$ we describe the initial object in the category of all $X$-generated $F$-inverse monoids $F$ for which $F/σ=G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_09256 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | $F$-inverse monoids as algebraic structures in enriched signature Auinger, K. Kudryavtseva, G. Szendrei, M. B. Group Theory 20M18, 20M07, 20M10 Every $F$-inverse monoid can be equipped with the unary operation which maps each element to the maximum element of its $σ$-class. In this enriched signature, the class of all $F$-inverse monoids forms a variety of algebraic structures. We describe universal objects in several classes of $F$-inverse monoids, in particular free $F$-inverse monoids. More precisely, for every $X$-generated group $G$ we describe the initial object in the category of all $X$-generated $F$-inverse monoids $F$ for which $F/σ=G$. |
| title | $F$-inverse monoids as algebraic structures in enriched signature |
| topic | Group Theory 20M18, 20M07, 20M10 |
| url | https://arxiv.org/abs/1905.09256 |