保持一个等价关系的部分一一变换半群的Green关系
Green's Relations on the Semigroup of One-One Partial Transfomations which Preserve an Equivalence
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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)∈dom α,xα=yα⇒x=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∈dom α,(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.Abstract: Let X be an arbitrary nonempty set and E an equivalence relation on X. Let PX denote the partial transformation semigroup on the set X. Recall that IX=α∈PX:(x,y)∈dom α,xα=yα⇒x=y.Then IX is a subsemigroup of PX called the symmetric inverse semigroup on X. Let IE(X)=α∈IX:x,y∈dom α,(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.
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