Related papers: Unit-regular and semi-balanced elements in various…

Let $T(X)$ (resp. L(V)) be the semigroup of all transformations (resp. linear transformations) of a set $X$ (resp. vector space $V$). For a subset $Y$ of $X$ and a subsemigroup $\mathbb{S}(Y)$ of $T(Y)$, consider the subsemigroup…

Let $X$ be an arbitrary set and let $T(X)$ denote the full transformation monoid on $X$. We prove that an element of $T(X)$ is unit-regular if and only if it is semi-balanced. For infinite $X$, we discuss regularity of the submonoid of…

Let $X$ be a nonempty set and let $T(X)$ be the full transformation semigroup on $X$. The main objective of this paper is to study the subsemigroup $\overline{\Omega}(X, Y)$ of $T(X)$ defined by \[\overline{\Omega}(X, Y) = \{f\in T(X)\colon…

Suppose that $X$ be a nonempty set. Denote by $\mathcal{T}(X)$ the full transformation semigroup on $X$. For $\varnothing \neq Z\subseteq Y\subseteq X$, let $\mathcal{T}(X,Y,Z)=\{\alpha \in \mathcal{T}(X): Y\alpha \subseteq Z \}$. Then…

Let $X$ be a nonempty set and $\mathcal{P}=\{X_i\colon i\in I\}$ a partition of $X$. Denote by $T(X)$ the full transformation semigroup on $X$, and $T(X, \mathcal{P})$ the subsemigroup of $T(X)$ consisting of all transformations that…

Let $X$ be a set and $\mathcal{T}_X$ be the full transformation semigroup on $X$. For a partition $\mathcal{P}$ of $X$, we consider semigroups $T(X, \mathcal{P}) = \{f\in \mathcal{T}_X| (\forall X_i\in \mathcal{P}) (\exists X_j \in…

Let $X$ be a nonempty set and $\mathcal{P}=\{X_i\colon i\in I\}$ be a partition of $X$. Denote by $T(X, \mathcal{P})$ the semigroup of all transformations of $X$ that preserve $\mathcal{P}$. In this paper, we study the semigroup…

Let $V$ be a vector space and $U$ a fixed subspace of $V$. We denote the semigroup of all linear transformations on $V$ under composition of functions by $L(V)$. In this paper, we study the semigroup of all linear transformations on $V$…

Let $X_n = \{1,2,\dots,n\}$ be a finite set $(n\geq 2)$ and $T_n$ the full transformation semigroup on $X_n$. For a positive integer $l\leq n-1$, we define $$T_n(l) = \{\alpha\in T_n \colon \forall x,y\in X_n,\, |x-y| = l \;\Rightarrow\;…

A quasi-semiregular element in a permutation group is an element that has a unique fixed point and acts semiregularly on the remaining points. Such elements were first studied in the context of automorphisms of graphs and occur naturally in…

Let $[n]=\{1,2,\ldots,n\}$ be a finite chain and let $\mathcal{T}_{n}$ be the semigroup of full transformations on $[n]$. Let $\mathcal{CT}_{n}=\{\alpha\in \mathcal{T}_{n}: (for ~all~x,y\in…

We prove that an hypersemigroup $H$ is regular if and only, for any fuzzy subset $f$ of $H$, we have $f\preceq f\circ 1\circ f$ and it is intra-regular if and only if, for any fuzzy subset $f$ of $H$, we have $f\preceq 1\circ f\circ f\circ…

Let $X$ be a nonempty set and $T(X)$ the full transformation semigroup on $X$. For any equivalence relation $E$ on $X$, define a subsemigroup $T_{E^*}(X)$ of $T(X)$ by $$ T_{E^*}(X)=\{\alpha\in T(X):\text{for all}\ x,y\in X, (x,y)\in…

Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the…

Semiclassical systems being symmetric under Lie group are studied. A state of a semiclassical system may be viewed as a set (X,f) of a classical state X and a quantum state f in the external classical background X. Therefore, the set of all…

Let $S$ be a semigroup and $\mathbb F$ be a field. For an ideal $J$ of the semigroup algebra ${\mathbb F}[S]$ of $S$ over $\mathbb F$, let $\varrho _J$ denote the restriction (to $S$) of the congruence on ${\mathbb F}[S]$ defined by the…

Let $a$ be a non-invertible transformation of a finite set and let $G$ be a group of permutations on that same set. Then $\genset{G, a}\setminus G$ is a subsemigroup, consisting of all non-invertible transformations, in the semigroup…

In this paper we study the regular semigroups weakly generated by a single element x, that is, with no proper regular subsemigroup containing x. We show there exists a regular semigroup $F_1$ weakly generated by x such that all other…

For a groupoid $S$ with elements $a$ and $b$, if $ba = a$, then $b$ is a left identity of $a$ and $a$ is a right zero of $b$. We define the left identity set of $a$ to be the set of all left identities of $a$ in $S$, and similarly for the…

We investigate the computational complexity for determining various properties of a finite transformation semigroup given by generators. We introduce a simple framework to describe transformation semigroup properties that are decidable in…