$F$-inverse monoids as algebraic structures in enriched signature
| Autor: | Maria Szendrei, Karl Auinger, Ganna Kudryavtseva |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Monoid
Pure mathematics Unary operation Group (mathematics) Algebraic structure General Mathematics Group Theory (math.GR) 20M18 20M07 20M10 Mathematics::Category Theory FOS: Mathematics Variety (universal algebra) Element (category theory) Signature (topology) Mathematics - Group Theory Mathematics Initial and terminal objects |
| Popis: | Every $F$-inverse monoid can be equipped with the unary operation which maps each element to the maximum element of its $\sigma$-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 $F/\sigma=G$. Comment: 21 pages |
| Databáze: | OpenAIRE |
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