Related papers: The structure of End($\mathcal{T}_n$)
Denote by $\mathcal T_n$ and $\mathcal S_n$ the full transformation semigroup and the symmetric group on the set $\{1,\ldots,n\}$, and $\mathcal E_n=\{1\}\cup(\mathcal T_n\setminus \mathcal S_n)$. Let $\mathcal T(X,\mathcal P)$ denote the…
In this paper we consider endomorphisms of an undirected cycle graph from Semigroup Theory perspective. Our main aim is to present a process to determine sets of generators with minimal cardinality for the monoids $wEnd(C_n)$ and $End(C_n)$…
In this paper, we investigate Polish semigroup topologies on the endomorphism monoids $\operatorname{End}(\mathbb{N},\leq)$ and $\operatorname{End}(\mathbb{Z},\leq)$. We introduce a new structural condition, property $\mathbb{XX}$, which…
For a group $G$ acting on a set $X$, let $\text{End}_G(X)$ be the monoid of all $G$-equivariant transformations, or $G$-endomorphisms, of $X$, and let $\text{Aut}_G(X)$ be its group of units. After discussing few basic results in a general…
We give a direct construction of a specific idempotent in the endomorphism algebra of a finite lattice $T$. This idempotent is associated with all possible sublattices of $T$ which are total orders.
In this paper, we characterize the monoid of endomorphisms of the semigroup of all monotone full transformations of a finite chain, as well as the monoids of endomorphisms of the semigroup of all monotone partial transformations and of the…
In this paper, we characterize the monoid of endomorphisms of the semigroup of all oriented full transformations of a finite chain, as well as the monoid of endomorphisms of the semigroup of all oriented partial transformations and the…
In this paper we consider endomorphisms of a finite directed path from monoid generators perspective. Our main aim is to determine the rank of the monoid $\wEnd\vec{P}_n$ of all weak endomorphisms of a directed path with $n$ vertices, which…
We study the semigroup of non-injective monoid endomorphisms of the semigroup $\boldsymbol{B}_{\omega}^{\mathscr{F}}$ with a two-elements family $\mathscr{F}$ of inductive nonempty subsets of $\omega$. We describe the structure of elements…
In this paper we study regular irreducible algebraic monoids over $\fldc$ equipped with the euclidean topology. It is shown that, in such monoids, the Green classes and the spaces of idempotents in the Green classes all have natural…
We sudy the behaviour of endomorphisms and automorphisms of groups involved in abelian group extensions. The main result can be stated as follows: Let $0\to N\to G\to Q \to 1$ be an abelian group extension. Then one has the following exact…
For a group $G$ and a finite set $A$, denote by $\text{End}(A^G)$ the monoid of all continuous shift commuting self-maps of $A^G$ and by $\text{Aut}(A^G)$ its group of units. We study the minimal cardinality of a generating set, known as…
Denote by PSelf(X) (resp., Self(X)) the partial (resp., full) transformation monoid over a set X, and by Sub(V) (resp., End(V)) the collection of all subspaces (resp., endomorphisms) of a vector space V. We prove various results that imply…
Ends and end cohomology are powerful invariants for the study of noncompact spaces. We present a self-contained exposition of the topological theory of ends and prove novel extensions including the existence of an exhaustion of a proper…
The rank of a semigroup is the cardinality of a smallest generating set. In this paper we compute the rank of the endomorphism monoid of a non-trivial uniform partition of a finite set, that is, the semigroup of those transformations of a…
We investigate endomorphism semirings of a finite semilattice with one least element and one greatest element such that all the other elements form an antichain. We construct some new finite simple semirings. Keywords: endomorphism…
In this paper we present general techniques for characterising minimal and maximal semigroup topologies on the endomorphism monoid $\operatorname{End}(\mathbb{A})$ of a countable relational structure $\mathbb{A}$. As applications, we show…
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…
Idempotents yield much insight in the structure of finite semigroups and semirings. In this article, we obtain some results on (multiplicatively) idempotents of the endomorphism semiring of a finite chain. We prove that the set of all…
We calculate the rank and idempotent rank of the semigroup $E(X,P)$ generated by the idempotents of the semigroup $T(X,P)$, which consists of all transformations of the finite set $X$ preserving a non-uniform partition $P$. We also classify…