Related papers: A remark on contracting inverse semigroups
We present some generalizations of the well-known correspondence, found by R. Exel, between partial actions of a group $G$ on a set $X$ and semigroup homomorphism of $S(G)$ on the semigroup $I(X)$ of partial bijections of $X,$ being $S(G)$…
We characterize trees as median algebras and semilattices by relaxing conservativeness. Moreover, we describe median homomorphisms between products of median algebras and show that Arrow type impossibility theorems for mappings from a…
A semigroup $S$ is called a permutable semigroup if $\alpha \circ \beta =\beta \circ \alpha$ is satified for all congruences $\alpha$ and $\beta$ of $S$. A semigroup is called a Putcha semigroup if it is a semilattice of archimedean…
We prove that if $S$ is an $E$-solid locally inverse semigroup, and $\rho$ is an inverse semigroup congruence on $S$ such that the idempotent classes of $\rho$ are completely simple semigroups then $S$ is embeddable into a…
We present a category equivalent to that of semi-Nelson algebras. The objects in this category are pairs consisting of a semi-Heyting algebra and one of its filters. The filters must contain all the dense elements of the semi-Heyting…
A semigroup $S$ is an equational domain if any finite union of algebraic sets over $S$ is algebraic. We prove that if an inverse semigroup $S$ is an equational domain in the extended language $\{\cdot,{}^{-1}\}\cup\{s|s\in S\}$ then $S$ is…
We show analogues of the classical Krein-Milman theorem for several ordered algebraic structures, especially in a semilattice (non-linear) framework. In that case, subsemilattices are seen as convex subsets, and for our proofs we use…
A sectionally pseudocomplemented poset P is one which has the top element and in which every principal order filter is a pseudocomplemented poset. The sectional pseudocomplements give rise to an implication-like operation on P which…
We consider the link and three-manifold invariants from arXiv:1912.02063, which are defined in terms of certain non-semisimple finite ribbon categories $\mathcal{C}$ together with a choice of tensor ideal and modified trace. If the ideal is…
To an inverse semigroup, we associate an \'etale groupoid such that its actions on topological spaces are equivalent to actions of the inverse semigroup. Both the object and the arrow space of this groupoid are non-Hausdorff. We show that…
A semigroup is \emph{amiable} if there is exactly one idempotent in each $\mathcal{R}^*$-class and in each $\mathcal{L}^*$-class. A semigroup is \emph{adequate} if it is amiable and if its idempotents commute. We characterize adequate…
Let $(S,\cdot)$ be a semigroup and $\mathfrak{m}$ be a $\sigma$-algebra on $S$. We say $(S,\cdot,\mathfrak{m})$ is a measurable semigroup if $\pi:S\times S\longrightarrow S$ by $\pi(x,y)=x\cdot y$ is a measurable function. In this paper ,…
Let $(G,w)$ be an undirected weighted graph. The group inverse of $(G,w)$ is the weighted graph with the adjacency matrix $A^{\#}$, where $A$ is the adjacency matrix of $(G,w)$. We study the group inverse of singular weighted trees. It is…
Let $S$ be a semigroup, $\Lambda$ a non-empty set and $P$ a mapping of $\Lambda$ into $S$. The set $S\times \Lambda$ together with the operation $\circ _P$ defined by $(s, \lambda)\circ _P(t, \mu )=(sP(\lambda)t, \mu )$ form a semigroup…
We demonstrate quasi-isometric rigidity for the product of a non-uniform rank one lattice and a nilpotent lattice. Specifically, we show that any finitely-generated group quasi-isometric to such a product is, up to finite noise, an…
The vertices of the Cayley graph of a finitely generated semigroup form a set of sites which can be labeled by elements of a finite alphabet in a manner governed by a nonnegative real interaction matrix, respecting nearest neighbor…
A basic result in semigroup theory states that every $C_0$-semigroup is quasi-contractive with respect to some appropriately chosen equivalent norm. This paper contains a counterpart of this well-known fact. Namely, by examining the…
A quasiconformal tree is a metric tree that is doubling and of bounded turning. We prove that every quasiconformal tree is quasisymmetrically equivalent to a geodesic tree with Hausdorff dimension arbitrarily close to 1.
This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…
If a graph has a non-singular adjacency matrix, then one may use the inverse matrix to define a (labeled) graph that may be considered to be the inverse graph to the original one. It has been known that an adjacency matrix of a tree is…