半群PO_(n)(k)的格林(星)关系及富足性  

The(star)-Green's relations and abundance of the semigroup PO_(n)(k)

作　　者：刘木村 高荣海 LIU Mu-cun;GAO Rong-hai(School of Mathematics Science,Guizhou Normal University,Guiyang 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《云南民族大学学报（自然科学版）》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)。

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.

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 

分 类 号：O152.7[理学—数学]