纯正半群上的一类偏序关系  

A Kind of Partial Orders on Orthodox Semigroups

作　　者：邵勇[1] 任苗苗[1] 

机构地区：[1]西北大学数学系,西安陕西710127

出　　处：《数学进展》2013年第4期458-464,共7页Advances in Mathematics（China）

基　　金：陕西省自然科学基金(No.2011JQ1017);西北大学科学研究基金(No.NC0925)

摘　　要：本文引入了右逆半群的自共轭强全子半群和局部极大锥形的概念.由自共轭强全子半群出发,构造出了右逆半群上的一类偏序关系,并由此给出了右逆半群上的自然偏序的新刻画.由纯正半群上存在最小逆半群同余的事实出发(用y表示最小的逆半群同余),证明了右逆半群S的全体局部极大锥形和商半群S/y上的全体左amenable偏序之间存在保序双射.In this paper, we introduce the concepts of self-conjugate strong fully subsemi- group and locally maximal cone of right inverse semigroup. We construct the partial orders on right inverse semigroup by self-conjugate strong fully subsemigroup and give a new characteri- zation of natural partial order on right inverse semigroup. It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. We prove that there exists an order- preserving bijection from the set of all locally maximal cones of right inverse semigroup S to the set of all left amenable partial orders on S/Y.

关 键 词：右逆半群 自共轭强全子半群 局部极大锥形 左amenable偏序 

分 类 号：O152.7[理学—数学]