Results 1 to 10 of about 418 (57)
Perfectly supportable semigroups are σ-discrete in each Hausdorff shift-invariant topology
Topological Algebra and its Applications, 2013 In this paper we introduce perfectly supportable semigroups and prove that they are \sigma-discrete in each Hausdorff shift-invariant topology. The class of perfectly supportable semigroups includes each subsemigroup S of the semigroup FRel(X) of ...
Banakh Taras, Guran Igor
doaj +3 more sources
Open Mathematics, 2021 Let T(X)T\left(X) be the full transformation semigroup on a set XX. For an equivalence EE on XX, let TE∗(X)={α∈T(X):∀x,y∈X,(x,y)∈E⇔(xα,yα)∈E}.{T}_{{E}^{\ast }}\left(X)=\left\{\alpha \in T\left(X):\forall x,y\in X,\left(x,y)\in E\iff \left(x\alpha ,y ...
Sangkhanan Kritsada
doaj +1 more source
Some results on semigroups of transformations with restricted range
Open Mathematics, 2021 Let XX be a non-empty set and YY a non-empty subset of XX. Denote the full transformation semigroup on XX by T(X)T\left(X) and write f(X)={f(x)∣x∈X}f\left(X)=\{f\left(x)| x\in X\} for each f∈T(X)f\in T\left(X). It is well known that T(X,Y)={f∈T(X)∣f(X)⊆Y}
Yan Qingfu, Wang Shoufeng
doaj +1 more source
On pomonoid of partial transformations of a poset
Open Mathematics, 2023 The main objective of this article is to study the ordered partial transformations PO(X){\mathcal{PO}}\left(X) of a poset XX. The findings show that the set of all partial transformations of a poset with a pointwise order is not necessarily a pomonoid ...
Al Subaiei Bana
doaj +1 more source
On semigroups of transformations that preserve a double direction equivalence
Open Mathematics, 2023 For a non-empty set XX, denote the full transformation semigroup on XX by T(X)T\left(X) and suppose that EE is an equivalence relation on XX. Evidently, TE∗(X)={α∈T(X)∣(x,y)∈Eif and only if(xα,yα)∈Efor allx,y∈X}{T}_{{E}^{\ast }}\left(X)=\left\{\alpha \in
Chen Hui, Liu Xin, Wang Shoufeng
doaj +1 more source
On a locally compact monoid of cofinite partial isometries of ℕ with adjoined zero
Topological Algebra and its Applications, 2022 Let 𝒞ℕ be a monoid which is generated by the partial shift α : n↦n +1 of the set of positive integers ℕ and its inverse partial shift β : n + 1 ↦n. In this paper we prove that if S is a submonoid of the monoid Iℕ∞ of all partial cofinite isometries of ...
Gutik Oleg, Khylynskyi Pavlo
doaj +1 more source
Regularity and abundance on semigroups of partial transformations with invariant set
Open Mathematics, 2023 Let P(X)P\left(X) be a partial transformation semigroup on a non-empty set XX. For a fixed non-empty subset YY of XX, let PT¯(X,Y)={α∈P(X)∣(domα∩Y)α⊆Y}.\overline{PT}\left(X,Y)=\left\{\alpha \in P\left(X)| \left({\rm{dom}}\hspace{0.33em}\alpha \cap Y ...
Pantarak Thapakorn, Chaiya Yanisa
doaj +1 more source
On idempotent generated semigroups [PDF]
, 2002 We provide short and direct proofs for some classical theorems proved by Howie, Levi and McFadden concerning idempotent generated semigroups of transformations on a finite set.Comment: three ...
Araújo, João
core +2 more sources
Ordered Regular Semigroups with Biggest Associates
Discussiones Mathematicae - General Algebra and Applications, 2019 We investigate the class BA of ordered regular semigroups in which each element has a biggest associate x† = max {y | xyx = x}. This class properly contains the class PO of principally ordered regular semigroups (in which there exists x⋆ = max {y | xyx ...
Blyth T.S., Santos M.H. Almeida
doaj +1 more source
Idempotent rank in the endomorphism monoid of a non-uniform partition [PDF]
, 2015 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 and enumerate
Dolinka, Igor +2 more
core +2 more sources