半群I_(n,r)的极大(逆)子半群  

The Maximal Inverse Subsemigroup of a Semigroup I_(n,r)

作　　者：肖坚 余江慧 罗永贵 XIAO Jian;YU Jiang-hui;LUO 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85-88,共4页Journal of Zunyi Normal University

基　　金：贵州师范大学校级项目“F-型(变换)半群及子半群的若干研究”(黔师新苗[2021]B08号);国家自然科学基金(地区科学基金)项目“黎曼流形间的双调和映射的若干问题研究”(11861022)。

摘　　要：设S_(n)和I_(n)分别是X_(n)={1,2,....n}上的对称群和对称逆半群.对0≤r≤n,令I(n,r)={α∈I_(n):im(α)≤r},则I(n,r)是对称逆半群I的双边理想.对0≤r≤n-1,考虑半群I_(n,r)=I(n,r)∪S_(n)的极大(逆)子半群的完全分类.证明了半群I_(n)的极大子半群和极大逆子半群是一致的.Let S_(n) and I_(n) be symmetric group and symmetric inverse semigroup on Xn={1,2,....n}respectively.For 0≤r≤n,put I(n,r)={α∈I_(n):im(α)≤r};I(n,r)are the two-sided ideals of symmetric inverse senigroup I_(n),For0≤r≤n-1,we need to consider complete classification of the maximal inverse subsemigroup of a semigroup I_(n,r)=I(n,r)∪S_(n).This paper proved that the maximal sub-semigroup and the maximal inverse subsemigroup of I_(n,r) are consistent.

关 键 词：对称群 对称逆半群 理想 极大子半群 极大逆子半群 

分 类 号：O152.7[理学—数学]