变换半群T_(SE)~(x0)(X)上的自然偏序

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英文篇名：Natural partial order on transformation semigroup T_(SE)~(x0)(X) 作者：刘葵 英文作者：LIU Kui;School of Science,Guizhou Institute of Technology; 关键词：自然偏序 ; 全变换半群 ; 相容 ; 正则元 英文关键词：natural partial order;;transformation semigroup;;compatible;;regular 中文刊名：NATR 英文刊名：Journal of Guizhou Normal University(Natural Sciences) 机构：贵州理工学院理学院; 出版日期：2014-08-15 出版单位：贵州师范大学学报(自然科学版) 年：2014 期：v.32;No.116 语种：中文; 页：NATR201404011 页数：4 CN：04 ISSN：52-5006/N 分类号：56-59

摘要

设X为一非空集合,T(X)为X上的变换半群,E为X上的一个等价关系,给出如下两个集合:Tx0(X)={α∈T(X):x0α=x0},Tx0SE(X)={α∈Tx0(X):x∈X,(x,xα)∈E}。证明了Tx0SE(X)为一正则半群,同时还讨论了Tx0SE(X)上的自然偏序结构及其左右相容性。
        Let X be a non-empty set,T(X) denote the full transformation semigroup on a set X. For an arbitrary equivalence relation E on X,we consider two sub semi-group of T( X) defined by:Tx0(X)= {α∈T(X):x0α = x0},Tx0SE(X) ={α∈Tx0(X):x∈X,(x,xα)∈E}It is shown that Tx0SE(X) is a regular semigroup,we also described the left compatibility and right compatibility of each element of Tx0SE(X) wich respect to this order.

引文

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