保持一个等价关系的部分一一变换半群的Green关系
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摘要
设X为任意非空集,E是X上的等价关系,PX表示集合X上的部分变换半群.IX={α∈PX:(x,y)∈domα,xα=yαx=y},且IX做成PX的一个子半群,称为对称逆半群.定义IE(X)={α∈IX:x,y∈domα,(x,y)∈E(xα,yα)∈E}.显然IE(X)关于部分变换的乘积(作为半群运算)生成一个半群,称为保持等价关系E的部分一一变换半群,它是IX的一个子半群.本文对IE(X)上的Green关系给出了完整的刻画.
Let Xbe an arbitrary nonempty set and Ean equivalence relation on X.Let PX denote the partial transformation semigroup on the set X.Recall that IX = {α ∈PX :(x,y)∈domα,xα =yαx =y}.Then IXis a subsemigroup of PX called the symmetric inverse semigroup on X.Let IE(X)= {α ∈IX :x,y ∈domα,(x,y)∈E(xα,yα)∈E}.Then IE(X)is a subsemigroup of IX.The complete discriptions for Green's relations on the semigroup IE(X)were given.
Let Xbe an arbitrary nonempty set and Ean equivalence relation on X.Let PX denote the partial transformation semigroup on the set X.Recall that IX = {α ∈PX :(x,y)∈domα,xα =yαx =y}.Then IXis a subsemigroup of PX called the symmetric inverse semigroup on X.Let IE(X)= {α ∈IX :x,y ∈domα,(x,y)∈E(xα,yα)∈E}.Then IE(X)is a subsemigroup of IX.The complete discriptions for Green's relations on the semigroup IE(X)were given.
引文
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[6]PEI Huisheng,DENG Weina.Naturally ordered semigroups of partial transformations preserving an equivalence relation[J].Communications in Algebra,2013,41(9):3308-3324.
[2]PEI Huisheng.Equivalences,α-semigroups andα-congruences[J].Semigroup Forum,1994,49(1):49-58.
[3]PEI Huisheng.Regularity and Green’s relations for semigroups of transformations that preserve an equivalence[J].Communications in Algebra,2005,33(1):109-118.
[4]PEI Huisheng.On the rank of the semigroup[J].Semigroup Forum,2005,70(1):107-117.
[5]裴惠生,邓伟娜.保持序和等价关系的自然偏序变换半群[J].数学学报:中文版,2012,55(2):235-250.PEI Huisheng,DENG Weina.Naturally ordered transformation semigroup preserving order and an equivalence relation[J].Acta Math Sinia,Chinese Series,2012,55(2):235-250.
[6]PEI Huisheng,DENG Weina.Naturally ordered semigroups of partial transformations preserving an equivalence relation[J].Communications in Algebra,2013,41(9):3308-3324.