半群D_(k)P_(n)的秩和平方幂等元秩  

On the rank and the quasi-idempotent rank of the semigroup D_(k)P_(n)

作　　者：张建国 余江慧 罗永贵 ZHANG Jianguo;YU Jianghui;LUO Yonggui(School of Mathematics Science,Guizhou Normal University,Guiyang 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《山东理工大学学报（自然科学版）》2023年第6期11-15,共5页Journal of Shandong University of Technology:Natural Science Edition

基　　金：贵州师范大学学术基金项目(黔师新苗[2021]B08号)。

摘　　要：设自然数n≥3,P_(n)和S_(n)是有限链X_(n)上的部分变换半群和对称群。对任意的正整数k满足1≤k≤n,令D_(k)是X_(n)上的k-局部二面体群,D_(k)P_(n)=D_(k)∪(P_(n)S_(n)),易证D_(k)P_(n)是部分变换半群P_(n)的子半群。通过分析半群D_(k)P_(n)的格林关系和幂等元,获得了半群D_(k)P_(n)的极小生成集和平方幂等元极小生成集,进一步,确定了半群D_(k)P_(n)的秩和平方幂等元秩。Let P_(n) and S_(n) be partial transformation semigroup and symmetry group on a finite chain X_(n),respectively,if natural number n≥3.For any positive integer k satisfying 1≤k≤n,let D_(k) be a k-locally dihedral group on X_(n),and let D_(k)P_(n)=D_(k)∪P_(n)\S_(n).It is easy to prove that D_(k)P_(n) is sub-semigroup of partial transformation semigroup P_(n).By analyzing the Green′s relation and the idempotent of the semigroup D_(k)P_(n),the minimal generating set and the minimal generating set of quasi-idempotent are obtained,and further the rank and the quasi-idempotent rank of the semigroup D_(k)P_(n) are determined.

关 键 词：部分变换半群 k-局部二面体群 (平方幂等元)极小生成集 (平方幂等元)秩 

分 类 号：O152.7[理学—数学]