摘要
设TX为集合X上的全变换半群,E为X上一个非平凡的等价关系.令TE(X)={f∈TX∶(a,b)∈E■(af,bf)∈E}则它在映射的合成运算下做成TX的一个子半群.称TE(X)为保等价关系变换半群.现讨论对于一个特殊情况,即X是有限的且E只有两个等价类,分别含有r,l(l>r>1)个元.我先讨论同胚群G的秩,然后考虑的TE(X)秩.结果发现,这时TE(X)有一组生成元,含有Crl+7个元素,从而确定了TE(X)的秩不超过Crl+7.
Let TX be the full transformation semigroup on the set X, for a nontrivial equivalence E on X, let TE（X）={f∈TX∶arbitary （a,b）∈E→（af,bf）∈E} is a subsemigroup of TX, it is called equivalence - preserving transformation semigroup. In this paper, we consider the rank of TE （X） for a special case that the set X is finite and the equivalence E has two classes ,each of them has r, l（ l 〉 r 〉 1 ） points. We first discuss the rank of the homemomorhism group G, then consider the rank of TE（X）. It is found that TE（X） has a generating set containing Cl^r＋7 elements, then we determine the rank of TE（X） is no more than Cl^r＋7.
出处
《贵州师范大学学报（自然科学版）》
CAS
2007年第4期73-75,共3页
Journal of Guizhou Normal University：Natural Sciences
基金
贵州省科技基金资助项目[(2007)2008号]
贵州师范大学学生科研研究基金资助
关键词
变换半群
等价关系
秩
映射
transformation semigroup
equivalence
rank
mapping
