Ajda Lemut Furlani: The free $F$-restriction semigroups

The free $F$-restriction semigroups

Ajda Lemut Furlani

Abstract: I will present a geometric model for the free $X$-generated $F$-restriction semigroup in the extended signature $(\cdot\,, ^+,{}^{\mathfrak{m}},\lambda)$, where the unary operation ${}^{\mathfrak{m}}$ maps an element $a$ to the maximum element ${a}^{\mathfrak{m}}$ of its $\sigma$-class, and the constant $\lambda$ is the unique left identity. This model is based on a certain quotient of the Cayley graph expansion of the free monoid $X^{ * }$ with respect to the extended set of generators $X \cup \overline{X^{ * }}$, where the generators from $\overline{X^{ * }} $ are in a bijection with the free monoid $X^{ * }$ and serve to capture the maximum elements of $\sigma$-classes of the quotient. I will also present models for the free $X$-generated strong and perfect $F$-restriction semigroups in the same extended signature. The constructed models enable us to solve the word problems for all the free objects under consideration.

This is joint work with Ganna Kudryavtseva and is based on our preprint available at https://arxiv.org/abs/2512.13332

The talk will be live and streamed.

Roman Drnovšek and Daniel Smertnig