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1
Content available remote

Semigroups of transformations restricted by an equivalence

100%
Mendes-Gonçalves S., Sullivan R.
Open Mathematics
|
2010
|
tom 8
|
nr 6
1120-1131
EN
Suppose σ is an equivalence on a set X and let E(X, σ) denote the semigroup (under composition) of all α: X → X such that σ ⊆ α ∘ α −1. Here we characterise Green’s relations and ideals in E(X, σ). This is analogous to recent work by Sullivan on K(V, W), the semigroup (under composition) of all linear transformations β of a vector space V such that W ⊆ ker β, where W is a fixed subspace of V.
2
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Infinite injective transformations whose centralizers have simple structure

100%
Konieczny J.
Open Mathematics
|
2011
|
tom 9
|
nr 1
23-35
EN
For an infinite set X, denote by Γ(X) the semigroup of all injective mappings from X to X under function composition. For α ∈ Γ(X), let C(α) = {β ∈ g/g(X): αβ = βα} be the centralizer of α in Γ(X). The aim of this paper is to determine those elements of Γ(X) whose centralizers have simple structure. We find α ∈ (X) such that various Green's relations in C(α) coincide, characterize α ∈ Γ(X) such that the $$ \mathcal{J} $$-classes of C(α) form a chain, and describe Green's relations in C(α) for α with so-called finite ray-cycle decomposition. If α is a permutation, we also find the structure of C(α) in terms of direct and wreath products of familiar semigroups.
3
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On Cayley graphs of completely 0-simple semigroups

81%
Wang S., Li Y.
Open Mathematics
|
2013
|
tom 11
|
nr 5
924-930
EN
We give necessary and sufficient conditions for various vertex-transitivity of Cayley graphs of the class of completely 0-simple semigroups and its several subclasses. Moreover, the question when the Cayley graphs of completely 0-simple semigroups are undirected is considered.
4
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The join of split graphs whose completely regular endomorphisms form a monoid

81%
Hou H., Song Y., Gu R.
Open Mathematics
|
2017
|
tom 15
|
nr 1
833-839
EN
In this paper, completely regular endomorphisms of the join of split graphs are investigated. We give conditions under which all completely regular endomorphisms of the join of two split graphs form a monoid.
5
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Perfectly supportable semigroups are σ-discrete in each Hausdorff shift-invariant topology

52%
Banakh T., Guran I.
Topological Algebra and its Applications
|
2013
|
tom 1
1-8
EN
In this paper we introduce perfectly supportable semigroups and prove that they are σ-discrete in each Hausdorff shiftinvariant topology. The class of perfectly supportable semigroups includes each semigroup S such that FSym(X) ⊂ S ⊂ FRel(X) where FRel(X) is the semigroup of finitely supported relations on an infinite set X and FSym(X) is the group of finitely supported permutations of X.
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