递减全变换半群的幂等元生成集深度  

The Depth of Idempotent Generating Set of Order-decreasing Full Transformation Semigroups

作　　者：钱承镠 杨秀良 QIAN Chengliu;YANG Xiuliang(School of Mathematics,Hangzhou Normal University,Hangzhou 311121,China)

机构地区：[1]杭州师范大学数学学院,浙江杭州311121

出　　处：《杭州师范大学学报（自然科学版）》2023年第3期305-311,共7页Journal of Hangzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11871186).

摘　　要：令Sing n为X n={1,2,…,n}上全变换半群的奇异部分.X n上递减全变换半群为S-n={α∈Sing n|xα≤x,x∈X n},S-n由幂等元生成,且被J*n-1里的n(n-1)/2个幂等元生成.文章进一步研究了S-n的幂等元深度问题,证明了E(J*n-1)是S-n的所有生成元集的交,给出了α∈S-n的E(J*n-1)-深度和S-n的全局E(J*n-1)-深度,以及α∈S-n的E(S-n)-深度和S-n的全局E(S-n)-深度.Let Sing n be the singular part of the full transformation semigroup on X n={1,2,…,n}.The semigroup of decreasing full transformation on X n is S-n={α∈Sing n|xα≤x,x∈X n}.S-n is generated by idempotent and n(n-1)/2 idempotents in J*n-1.On this basis,the depth problem of idempotent elements of S-n is investigated.It is proved that E(J*n-1)is the intersection of all generating set of S-n,and the E(J*n-1)-depth of anyα∈S-n and global E(J*n-1)-depth of S-n are obtained,as well as the E(S-n)-depth of anyα∈S-n and global E(S-n)-depth of S-n.

关 键 词：全变换半群 递减全变换半群 幂等元深度 

分 类 号：O152.7[理学—数学]