Related papers: $F$-inverse monoids as algebraic structures in enr…

An inverse monoid $S$ is called $F$-inverse if each $\sigma$-class of $S$, where $\sigma$ is the minimum group congruence of $S$, has a maximum element with respect to the natural order of $S$. Since the property of an inverse monoid being…

Motivated by recent interest to $F$-inverse monoids, on the one hand, and to restriction and birestriction monoids, on the other hand, we initiate the study of $F$-birestriction monoids as algebraic structures in the enriched signature…

We show that the universal $X$-generated $F$-inverse monoid $F(G)$, where $G$ is an $X$-generated group, introduced by Auinger, Szendrei and the first-named author, arises as a quotient inverse monoid of the Margolis-Meakin expansion $M(G,…

We show that the category of $X$-generated $E$-unitary inverse monoids with greatest group image $G$ is equivalent to the category of $G$-invariant, finitary closure operators on the set of connected subgraphs of the Cayley graph of $G$.…

We introduce the inverse monoid of inner partial automorphisms of a semigroup -- a tool that associates to every semigroup an inverse semigroup. When the semigroup is a group, this inverse semigroup is isomorphic to the group of inner…

It is known that an inverse monoid $M$ is E-unitary if and only if the following diagram is an extension: $E(M) \to M \to M/\sigma$, where $E(M)$ is the semilattice of idempotents and $M/\sigma$ is the minimal group quotient. F-inverse…

We continue the study of the structure of general subgroups (in particular maximal subgroups, also known as group $\mathcal{H}$-classes) of special inverse monoids. Recent research of the authors has established that these can be quite…

A partial automorphism of a finite graph is an isomorphism between its vertex induced subgraphs. The set of all partial automorphisms of a given finite graph forms an inverse monoid under composition (of partial maps). We describe the…

We study the maximal subgroups (also known as group $\mathcal{H}$-classes) of finitely presented special inverse monoids. We show that the maximal subgroups which can arise in such monoids are exactly the recursively presented groups, and…

In this paper we show that polycyclic monoids are universal objects in the class of graph inverse semigroups. In particular, we prove that a graph inverse semigroup $G(E)$ over a directed graph $E$ embeds into the polycyclic monoid…

Finite-above inverse monoids are a common generalization of finite inverse monoids and Margolis--Meakin expansions of groups. Given a finite-above $E$-unitary inverse monoid $M$ and a group variety $\mathit{U}$, we find a condition for $M$…

We define a class of inverse monoids having the property that their lattices of principal ideals naturally form an MV-algebra. We say that an arbitrary MV-algebra can be co-ordinatized if it is isomorphic to one constructed in this way from…

A countably infinite Boolean inverse monoid that can be written as an increasing union of finite Boolean inverse monoids (suitably embedded) is said to be of finite type. Borrowing terminology from $C^{\ast}$-algebra theory, we say that…

A special inverse monoid is one defined by a presentation where all the defining relations have the form $r = 1$. By a result of Ivanov Margolis and Meakin the word problem for such an inverse monoid can often be reduced to the word problem…

A prefix monoid is a finitely generated submonoid of a finitely presented group generated by the prefixes of its defining relators. Important results of Guba (1997), and of Ivanov, Margolis and Meakin (2001), show how the word problem for…

We curry the elementary arithmetic operations of addition and multiplication to give monotone injections on N, and describe & study the inverse monoids that arise from also considering their generalised inverses. This leads to well-known…

We study the geometry of algebraic monoids. We prove that the group of invertible elements of an irreducible algebraic monoid is an algebraic group, open in the monoid. Moreover, if this group is reductive, then the monoid is affine. We…

Given an action of a monoid $T$ on a ring $A$ by ring endomorphisms, and an Ore subset $S$ of $T$, a general construction of a fractional skew monoid ring $S^{\rm op} * A * T$ is given, extending the usual constructions of skew group rings…

Let $<X>$ be the free monoid on a generating set $X$, and suppose one adjoins to $<X>$ universal 2-sided inverses to a finite set $S$ of its elements. We note an elementary algorithm which yields a normal form for elements of the resulting…

A fully invarient congruence relations on the free algebra on a given type induces a variety of the given type. In contrast, a congruence relation of the free algebra provides algebra of that type. This algebra is given by a so-called…