摘要
研究的CDOn是自然序集X_n={1,2,3,…,n}(n≥4)上的保序且保压缩或保反序且保压缩有限奇异变换半群,记K_D~*(n,r)={α∈CDO_n:|Imα|≤r}为半群CDOn的双边星理想.对1≤r≤n一1,刻划了K_D~*(n,r)是由秩为r的元素生成的且当r=1时,rank(K_D~*(n,r))=n;当2≤r≤n一1时,rank(K_D~*(n,r))=C_(n-1)^(r-1).进一步证明了当l=r时,r(K_D~*(n,r),K_D~*(n,l))=0且当1≤l<r时,r(K_D~*(n,r),K_D~*(n,l))=C_(n-1)^(r-1)
Let CDOn be the semigroups of order-preserving and compressing or order- reversing and compressing finite singular transformations on the natural order set Xn = {1,2,3,… ,n}（n ≥ 4）, and let K＊D（n,r） = {α∈CDOn ： [Imα] ≤ r} be the two-sided star ideal of the semigroup CDOn. In this paper, the semigroup K＊D （n, r） generated by elements of rank r is characterized. We proved that rank（K＊D（n,r）） is n if r = 1 and is Cr-1 n-1 if 2≤ r ≤n- 1. Furthermore, it is shown that r（K＊D）（n,r）,K＊D（n,l）） is 0 if l = r and is Cr-1 n-1 if1≤l≤r.
出处
《数学的实践与认识》
北大核心
2015年第12期240-245,共6页
Mathematics in Practice and Theory
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
关键词
保序
保反序
压缩
奇异变换半群
秩和相关秩
order-preserving
order-reversing
compression
singular transformation semi-group
rank and relative rank
