正则半群上的Amenable偏序关系  

Amenable partial orders on regular semigroups

作　　者：邵勇[1] 赵宪钟[2] 郭聿琦[3] 

机构地区：[1]西北大学数学系,西安710127 [2]江西师范大学数学与信息科学学院,南昌330022 [3]西南大学数学系,重庆400715

出　　处：《兰州大学学报（自然科学版）》2013年第3期389-394,399,共7页Journal of Lanzhou University(Natural Sciences)

基　　金：中国博士后科学研究基金项目(2011M501466);江西省自然科学基金项目(2010GZS0093);陕西省自然科学基金项目(2011JQ1017);陕西省教育厅自然科学基金项目(2012JK0872)

摘　　要：给出了正则半群上Amenable偏序的一些刻画;证明了正则半群S上能够装有Amenable偏序当且仅当S是局部逆半群;完整地描述了完全正则半群上的Amenable偏序;证明了具有逆断面的广义逆半群上的Amenable偏序可被其逆断面上的Amenable偏序所唯一确定.Some characterizations of amenable partial orders on a regular semigroup were first given;Next,it was proved that an amenable partial order can be imposed on a regular semigroup S if and only if S is a locally inverse semigroup.Also,a complete description of an amenable partial order was given on a completely regular semigroup,provided that S be a generalized inverse semigroup with an inverse transversal.At last,the relations between the amenable partial orders on inverse transversal and amenable partial orders on S were uncovered and it was proved that an amenable partial order on inverse transversal can be uniquely extended to an amenable partial order on S.

关 键 词：正则半群 局部逆半群 纯正半群 Amenable偏序 

分 类 号：O152.7[理学—数学]