李建华, 孙垒. 一类夹心变换半群的正则元[J]. 信阳师范学院学报(自然科学版), 2016, 29(3): 313-315. DOI: 10.3969/j.issn.1003-0972.2016.03.001
引用本文: 李建华, 孙垒. 一类夹心变换半群的正则元[J]. 信阳师范学院学报(自然科学版), 2016, 29(3): 313-315. DOI: 10.3969/j.issn.1003-0972.2016.03.001
LI Jianhua , SUN Lei . Regular Elements of a Kind of Sandwich Transformation Semigroups[J]. Journal of Xinyang Normal University (Natural Science Edition), 2016, 29(3): 313-315. DOI: 10.3969/j.issn.1003-0972.2016.03.001
Citation: LI Jianhua , SUN Lei . Regular Elements of a Kind of Sandwich Transformation Semigroups[J]. Journal of Xinyang Normal University (Natural Science Edition), 2016, 29(3): 313-315. DOI: 10.3969/j.issn.1003-0972.2016.03.001

一类夹心变换半群的正则元

Regular Elements of a Kind of Sandwich Transformation Semigroups

  • 摘要: 设TX是非空集合X上全变换半群,E是X上等价关系,则T∃(X)= f∈T:∀x,y∈X,(f(x),f(y))∈E⇒(x,y)∈E是T的反射等价关系的子半群.取定θ∈T∃(X),在T∃(X)上定义新的运算°为f°g=fθg,其中fθg表示一般意义上映射f、θ、g的复合.关于这个运算°,T∃(X)成为夹心变换半群T∃(X;θ).本文刻画了它的正则元,给出了T∃(X;θ)是正则半群的充要条件.

     

    Abstract: Let TX be the full transformation semigroup on a nonempty set X and E be an equivalence on X. Then T(X)=f∈TX:x,y∈X,(f(x),f(y))∈E(x,y)∈E is a subsemigroup of TX of transformations reflecting the equivalence E. Fix an element θ∈T(X) and define an operation ° on T(X) by f°g=fθg where fθg denotes the composition of the maps g,θ and f in the usual sense. With respect to the new operation °, T(X) forms a new semigroup which is called a sandwich semigroup of T(X) and denoted by T(X;θ).  The regular elements of the sandwich transformation semigroup T(X;θ) were characterized and a necessary and sufficient condition for the regular semigroup T(X;θ) was presented. 

     

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