Related papers: Almost perfect restriction semigroups

Let $G$ be a right-angled Artin group with defining graph $\Gamma$ and let $H$ be a finitely generated group quasi-isometric to $G(\Gamma)$. We show if $G$ satisfies (1) its outer automorphism group is finite; (2) $\Gamma$ does not have…

Let $\mathcal S \subseteq \mathbb Z^m \oplus T$ be a finitely generated and reduced monoid. In this paper we develop a general strategy to study the set of elements in $\mathcal S$ having at least two factorizations of the same length,…

In this paper, we investigate some characteristic features of holomorphic semigroups. In particular, we investigate nice examples of holomorphic semigroups whose every left or right ideal includes minimal ideal. These examples are compact…

It is well-known that a C-monoid is completely integrally closed if and only if its reduced class semigroup is a group and if this holds, then the C-monoid is a Krull monoid and the reduced class semigroup coincides with the usual class…

In this paper we characterize the monoid congruences of commutative semigroups by the help of the notion of the separator of subsets of semigroups. We show that every monoid congruence of a commutative semigroup S can be constructed by the…

Let $S$ be a right group. Then there exist two congruences $\sim$ and $\equiv$ on $S$ such that $S$ is the product of its quotient semigroups $S/{\sim}$ and $S/{\equiv}$, where $S/{\sim}$ is a group and $S/{\equiv}$ is a right zero…

Let $S$ be a reduced $E$-Fountain semigroup. If $S$ satisfies the congruence condition, there is a natural construction of a category $\mathcal{C}$ associated with $S$. We define a $\Bbbk$-module homomorphism $\varphi:\Bbbk…

Inspired by Kalton and Wood's work on group algebras, we describe almost completely contractive algebra homomorphisms from Fourier algebras into Fourier-Stieltjes algebras (endowed with their canonical operator space structure). We also…

We improve on earlier results on the closure under free products of the class of automaton semigroups. We consider partial automata and show that the free product of two self-similar semigroups (or automaton semigroups) is self-similar (an…

We prove a structure theorem for finite perfect two-sided skew braces. The main tool is a central product theory for skew braces, developed here in both external and internal form; we show that these two constructions are equivalent. Our…

In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…

To each meet-semilattice $E$ is associated an inverse semigroup $T_{E}$ called the Munn semigroup of $E$. We generalise this construction by replacing the meet-semilattice $E$ by a presheaf of sets $X$ over a meet-semilattice. The inverse…

The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…

Two groups have a common model geometry if they act properly and cocompactly by isometries on the same proper geodesic metric space. The Milnor-Schwarz lemma implies that groups with a common model geometry are quasi-isometric; however, the…

In this paper we develop a new groupoid-based structure theory for the class of regular $*$-semigroups. This class occupies something of a `sweet spot' between the important classes of inverse and regular semigroups, and contains many…

We define a notion of a rotund quasi-uniform space and describe a new direct construction of a (right-continuous) quasi-pseudometric on a (rotund) quasi-uniform space. This new construction allows to give alternative proofs of several…

In the paper we investigate the semigroup of monotone co-finite partial homeomorphisms of the space of the usual real line $\mathbb{R}$. We prove that the inverse semigroup $\mathscr{P\!\!H}^+_{\!\!\operatorname{\textsf{cf}}}\!(\mathbb{R})$…

A 1-factorization $\mathcal{M} = \{M_1,M_2,\ldots,M_n\}$ of a graph $G$ is called perfect if the union of any pair of 1-factors $M_i, M_j$ with $i \ne j$ is a Hamilton cycle. It is called $k$-semi-perfect if the union of any pair of…

A countable, bounded degree graph is almost finite if it has a tiling with isomorphic copies of finitely many F\o lner sets, and we call it strongly almost finite, if the tiling can be randomized so that the probability that a vertex is on…

Let $G$ be a right-angled Artin group with $|\mathrm{Out}(G)|<+\infty$. We prove that if a countable group $H$ with bounded torsion is measure equivalent to $G$, with an $L^1$-integrable measure equivalence cocycle towards $G$, then $H$ is…