半群P_n,r的极大(正则)子半群  

The Maximal (Regular) Subsemigroups of Semigroup Pn,r

作　　者：杨平平 张梁松 罗永贵 

机构地区：[1]贵州师范大学数学科学学院,贵州 贵阳

出　　处：《理论数学》2023年第6期1822-1828,共7页Pure Mathematics

摘　　要：设Sn和Pn分别是Xn={1,2,…,n}上的对称群和部分变换半群。对0≤r≤n,令P(n,r)={α∈Pn:|im(α)≤r},则P(n,r)是部分变换半群Pn的子半群。对0≤r≤n-1,考虑半群Pn,r=Pn,r∪Sn的极大(正则)子半群。通过对半群Pn,r格林关系的分析进一步,获得了半群Pn,r的极大子半群和极大正则子半群是一致的。Let Sn and Pn be symmetric group and partial transformation semigroup on Xn={1,2,…,n}, respectively. For 0≤r≤n, put P(n,r)={α∈Pn:|im(α)≤r}, then the set P(n,r) are the subsemigroups of . For 0≤r≤n-1. In this paper, the maximal (regular) subsemigroups of the semigroup Pn,r=Pn,r∪Sn has been considered. In addition, by analyzing the Green’s relations, this paper proved that the maximal subsemigroups and the maximal regular subsemigroups of Pn,r coincide.

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：O15[理学—数学]