Expansions of monoids

We discuss expansions of monoids in the class of two-sided restriction monoids. For a monoid $M$ and a class of partial actions of $M$ determined by a set, $R$, of identities, we define $FR_R(M)$ to be the universal $M$-generated two-sided restriction monoid with respect to partial actions of $M$ determined by $R$. This is an $F$-restriction monoid which (for a certain $R$) generalizes the Birget-Rhodes prefix expansion of a group.  We  explain that  $FR_R(M)$ can be coordinatized as a semidirect product of the idempotent semilattice of a similarly defined inverse monoid, partially acted upon by $M$. As a special case, this yields the result by Fountain, Gomes and Gould on the structure of the free two-sided restriction monoid. We also present some interesting particular cases and examples.

Date and Venue

Start Date
Online Zoom meeting
End Date


Ganna Kudryavtseva

Speaker's Institution

Ljubljana University, Slovenia



Semigroups, Automata and Languages