| 关于OI_n和DOI_n的理想的生成集及其秩 |
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| 引用本文： | 罗永贵,游泰杰,高荣海.关于OI_n和DOI_n的理想的生成集及其秩[J].贵州师范大学学报(自然科学版),2012,30(2):54-58. |
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| 作者姓名： | 罗永贵 游泰杰 高荣海 |
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| 作者单位： | 1. 贵州师范大学数学与计算机科学学院,贵州贵阳,550001
2. 贵州师范大学数学与计算机科学学院,贵州贵阳550001／贵州师范大学学报编辑部,贵州贵阳550001 |
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| 基金项目： | 基金项目:贵州省科技基金资助(黔科合J字LKS |
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| 摘 要： | 设Xn={1,2,3,…,n}(n≥3)并赋予自然序,OIn为Xn上的一切保序严格部分一一变换半群,DOIn为Xn上的一切保序或保反序严格部分一一变换半群.分别记OIn,DOIn的理想为K(n,r)=α∈OIn:|imα|≤{r},KD(n,r)={α∈D OIn:|imα|≤r}.刻划了K(n,r)=或KD(n,r)=当且仅当与I相伴的有向图Γ(I)是强连通的.同时证明了rank(K(n,r))=Crn和rank(KD(n,r))=Crn,其中0≤r≤n-1.
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| 关 键 词： | 对称逆半群 子半群 保序变换 保反序变换 理想 极小生成集 秩 |
Systems of generators and ranks of ideals of OIn and DOIn |
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| LUO Yong-gui,YOU Tai-jie,GAO Rong-hai.Systems of generators and ranks of ideals of OIn and DOIn[J].Journal of Guizhou Normal University(Natural Sciences),2012,30(2):54-58. |
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| Authors: | LUO Yong-gui YOU Tai-jie GAO Rong-hai |
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| Institution: | 1,2(1.Department of Mathematics and Computer Science,Guizhou Normal University,Guiyang,Guizhou 550001,China; 2.Journal Editorial Department,Guizhou Normal University,Guiyang,Guizhou 550001,China) |
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| Abstract: | Let Xn=1,2,3,…,nn≥3 ordered in the standard way,OIn be the semigroup of all order-preserving the strict partial one-to-one transformations on the set Xn and DOIn be the semigroup of all order-preserving or order-reversing the strict partial one-to-one transformations on the set Xn.Denoted Kn,r=α∈OIn:|imα|≤r be ideals of OIn and KDn,r=α∈DOIn:|imα|≤r be ideals of DOIn.In this paper,we characterize the Kn,r= or KDn,r= if and only if the directed digraph ΓI is strongly connected.At the same time,it is show that rank(K(n,r))=Crn and rank(KD(n,r))=Crn,where 0≤r≤n-1. |
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| Keywords: | symmetric inverse semigroup subsemigroup order-preserving transformation order-reversing transformation ideals minimal generating set rank |
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