半群(L)(F)(n,r)的幂等元秩
On the rank of semigroup(L)(F)(n,r)
龚何余 1舒琴 1赵平1
作者信息
- 1. 贵州师范大学数学科学学院,贵州贵阳 550001
- 折叠
摘要
设(F)n是Xn={1,2,…,n｝上的全变换半群,对任意1≤r≤n,令(F)(n,r)={α∈(F)n:iα=i,(˅)i∈｛1,2,…,r｝｝,则(F)(n,r)是(F)n的子半群.本文将研究半群(F)(n,r)的核(L)(F)(n,r)=<E((F)(n,r))>,其中E((F)(n,r))={α∈(F)(n,r)∶α2=α｝,通过对(F)(n,r)幂等元的分析,得到半群(L)(F)(n,r)的秩和幂等元秩都为(n-r)(n-r-1)/2+r(n-r)+1.
Abstract
Let (F)n be the full transformation semigroup on Xn=｛ 1,2,…,n ｝.Let 1 ≤ r≤ n,put(F)(n,r)={α∈(F)n∶iα=i,(˅)i∈｛1,2,…,r｝｝,it is obvious that the semigroup (F)(n,r) is subsemigroup of (F)n.In the paper,we study the core(L)(F)(n,r)=<E((F)(n,r))>of the semig-roup (F)(n,r),where E((F)(n,r))={α∈(F)(n,r)∶α2=α｝,by analyzing idempotents of the semigroup (F)(n,r),we prove that the rank and idempotent rank of semigroup(L)(F)(n,r)are both equal to(n-r)(n-r-1)/2+r(n-r)+1.
关键词
变换半群/核/固定集/幂等元秩Key words
transformation semigroup/core/fixed set/idempotent rank引用本文复制引用
基金项目
国家自然科学基金资助项目(12261022)
出版年
2024
NETL
NSTL
万方数据