Some remarks on F-inverse monoids

An inverse monoid $M$ is $F$-inverse if every $\sigma$-class $a\sigma$ admits a greatest element $a^\mathfrak{m}$ with respect to the natural partial order on $M$ ($\sigma$ denotes the smallest group congruence on $M$). An $F$-inverse monoid is necessarily $E$-unitary and such structures have attracted considerable attention. I intend to discuss the following topics:

$F$-inverse monoids with enriched signature: as algebraic structures of type $(2,1,1,0)$ (the second unary operation being $a\mapsto a^\mathfrak{m}$) the class of $F$-inverse monoids forms a variety (M. Kinyon). I shall present models of free $F$-inverse monoids and, more generally, universal objects in similarly defined categories (joint work with G. Kudryavtseva and M. B. Szendrei).

status of the Henckell--Rhodes problem (Does every finite inverse monoid admit a finite $F$-inverse cover?)

a possible extension of the Henckell--Rhodes problem (Is there an expansion from the category of finite inverse monoids to the category of finite $F$-inverse monoids?)

Date and Venue

Start Date
Venue
Online Zoom meeting
End Date

Speaker

Karl Auinger

Speaker's Institution

University of Vienna, Faculty of Mathematics

Files

Area

Semigroups, Automata and Languages

Financiamento