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arXiv · 1905.09256

$F$-inverse monoids as algebraic structures in enriched signature

K. Auinger·G. Kudryavtseva·M. B. Szendrei
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Abstract

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 $F/\sigma=G$.

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K. Auinger, G. Kudryavtseva, M. B. Szendrei. 2019-05-22. $F$-inverse monoids as algebraic structures in enriched signature. https://doi.org/10.1512/iumj.2021.70.8685

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