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The article is devoted to holomorphic and meromorphic functions of quaternion and octonion variables. New classes of quasi-conformal and quasi-meromorphic mappings are defined and investigated. Properties of such functions such as their…
We use semigroup theory to describe the group of automorphisms of some semigroups of interest in holomorphic dynamical systems. We show, with some examples, that representation theory of semigroups is related to usual constructions in…
Cross-connection is a construction of regular semigroups using certain categories called normal categories which are abstractions of the partially ordered sets of principal left (right) ideals of a semigroup. We describe the…
The notion of semifunctor between categories, due to S. Hayashi (1985), is defined as a functor that does not necessarily preserve identities. In this paper we study how several properties of functors, such as fullness, full faithfulness,…
We develop the theory of transformation semigroups that have degree 2, that is, act by partial functions on a finite set such that the inverse image of points have at most two elements. We show that the graph of fibers of such an action…
Green's relations on the deformed finite inverse symmetric semigroup $\mathcal{IS}_n$ and the deformed finite symmetric semigroup $\mathcal{T}_n$ are described.
Let $G$ be a semiabelian variety defined over an algebraically closed field $K$ of prime characteristic. We describe the intersection of a subvariety $X$ of $G$ with a finitely generated subgroup of $G(K)$.
We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between…
In this study we introduce the notions of semi-homotopy of semi-continuous maps and of semi-paths. We also construct a group structure, which will be called semi-fundamental group, using semi-loops and explore some properties of…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
In this paper we give an algebraic characterization of assemblies in terms of bands of groups. We also consider substructures and homomorphisms of assemblies. We give many examples and counterexamples.
We study the connection between small-overlap conditions and automaticity of semigroups. We restrict the discussion to conditions that imply embeddability and under which each relation decomposes into at least seven pieces. For these…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in…
We describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all transformation…
We classify minimal transitive subsemigroups of the finitary inverse symmetric semigroup modulo the classification of minimal transitive subgroups of finite symmetric groups; and semitransitive subsemigroups of the finite inverse symmetric…
We consider semigroups of continuous, surjective, locally injective maps of a compact metric space, and whether such semigroups admit a transfer operator.
Let G be a group which is hyperbolic relative to a collection of subgroups A, and it is also hyperbolic relative to a collection of subgroups B. Suppose that the collection A contains B. We characterize, for subgroups of G, when…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
Double semigroups have two associative operations $\circ, \bullet$ related by the interchange relation: $( a \bullet b ) \circ ( c \bullet d ) \equiv ( a \circ c ) \bullet ( b \circ d )$. Kock \cite{Kock2007} (2007) discovered a…
We determine the structure of the intersection of a finitely generated subgroup of a semiabelian variety $G$ defined over a finite field with a closed subvariety $X\subset G$.