半群PS(n,r)的极大子半群  

The Maximal Subsemigroups of Semigroup PS(n,r)

作　　者：杨平平 张梁松 罗永贵 YANG Ping-ping;ZHANG Liang-song;LUOs Yong-gui(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：《遵义师范学院学报》2024年第2期78-80,共3页Journal of Zunyi Normal University

基　　金：贵州师范大学学术基金项目(黔师新苗[2021]B08号);国家自然科学基金项目(11861022)。

摘　　要：设S_(n),T_(n),P_(n)和P_(n)\T_(n)分别是X_(n)={1,2,...,n}上的对称群、全变换半群、部分变换半群和严格部分变换半群.对0≤r≤n,令SP(n,r)={α∈P_(n)\T_(n):im(α)≤r},则SP(n,r)是部分变换半群P_(n)的双边理想.对0≤r≤n-1,考虑半群的极大子半群PS(n,r)=P(n,r)∪S_(n).进一步,获得了半群PS(n,r)的极大子半群和极大正则子半群是一致的.Let S_(n)T,P_(n)and P_(n)\T_(n)be symmetric group,full transformation semigroup,partial transformation semigroup and the strictly par-tial trans formation semigroup on X_(n)={1,2,....n}respectively.For 0≤r≤n,put SP(n,r)={α∈P_(n)\T_(n):im(α)≤r},SP(n,r)are the two-sided ideals of P_(n).For0≤r≤n-1,the maximal(regular)subsemigroups of the semigroup PS(n,r)=P(n,r)U S_(n)has been considered in this paper.In addition,this paper proved that the maximal subsemigroups and the maximal regular subsemigroups of are consistent.

关 键 词：部分变换半群 正则半群 理想 极大子半群 极大正则子半群 

分 类 号：O152.7[理学—数学]