摘要
设自然数n≥3,RCDOn是有限链[n]上的正则保反序且压缩奇异变换半群.对任意的r(1≤r≤n-1),记W_D(n,r)={α∈RCDO_n:|Im(α)|≤r}为半群RCDO_n的双边理想.通过对其非群元和格林关系的分析,分别获得了半群W_D(n,r)的极小非群元生成集、非群元秩和非幂等元秩.进一步确定了当1≤l≤r时,半群W_D(n,r)关于其理想W_D(n,l)的相关秩.
Let RCDOn be the semigroup of all regular order-reversing and compressing singular transformations on a finite-chain [n] for each n≥3,and WD(n,r) ={α∈RCDOn:|Ima(α) | ≤r| be the two-sided ideal of the semigroup RCDOn for an arbitrary integer r such that 1 ≤r≤≤n-1.By analyzing the non-group elements and Green's relations,we obtain the minimal non-group elements generating set,non-group rank and non-idempotent rank of the semigroup WD (n,r).Furthermore,the relative rank of the semigroup WD(n,r) with respect to itself ideal WD(n,l) is determined for 1 ≤l≤r.
出处
《四川师范大学学报(自然科学版)》
CAS
北大核心
2017年第3期308-312,共5页
Journal of Sichuan Normal University(Natural Science)
基金
贵州省科学技术基金-贵州师范大学联合科技基金(黔科合LH字(2014)7056号)
关键词
保反序
正则压缩
奇异变换半群
非群元秩和非幂等元秩
相关秩
order-reversing
regular compression
singular transformation semigroup
non-group rank and non-idempotent rank
relative rank