摘要
设P_(n)和PO_(n)分别是有限链[n]上的部分变换半群和保序部分变换半群.对任意1≤k≤n,令PO_(n)(k)={α∈PO_(n)(k):■x∈dom(α),x≤k■xα≤k},则PO_(n)(k)是P_(n)的子半群.通过分析半群PO_(n)(k)中的元素,获得了半群PO_(n)(k)的格林关系和格林星关系.进一步讨论了:当1≤k≤n-1时,半群PO_(n)(k)是非正则富足半群.
Let P_(n)and PO_(n)be partial transformation semigroup and order-preserving partial transformation semig⁃roup on a finite chain[n],respectively.For all 1≤k≤n,let PO_(n)(k)={α∈PO_(n)(k):■x∈dom(α),x≤k■xα≤k},then PO_(n)(k)is a subsemigroup of P_(n).By analyzing the elements of semigroup PO_(n)(k),the Green's rela⁃tions and the star-Green's relation of semigroup PO_(n)(k)are obtained,respectively.Furthemore,it is discussed that the semigroup PO_(n)(k)is an irregular abundant semigroup when 1≤k≤n-1.
作者
刘木村
高荣海
LIU Mu-cun;GAO Rong-hai(School of Mathematics Science,Guizhou Normal University,Guiyang 550025,China)
出处
《云南民族大学学报（自然科学版）》
CAS
2023年第5期652-657,共6页
Journal of Yunnan Minzu University:Natural Sciences Edition
基金
贵州师范大学学术新苗基金(黔师新苗[2021]B08号)。
关键词
保序变换半群
格林关系
格林星关系
正则元
非正则富足半群
order-preserving transformation semigroup
Green's relations
star-Green's relation
regular element
irregular abundant semigroup
