Locally Inverse Semigroups with Inverse Transversals  

具有逆断面的局部逆半群(英文)

作　　者：邵勇 赵宪钟 

机构地区：[1]Department of Mathematics,Northwest University [2]College of Mathematics and Information Science,Jiangxi Normal University

出　　处：《Journal of Mathematical Research and Exposition》2009年第4期599-606,共8页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China(No.10471112);the Natural Science Foundation of Education Committee of Shaanxi Province(No.07JK413)

摘　　要：Let S be a locally inverse semigroup with an inverse transversal S°.In this paper,we construct an amenable partial order on S by an R-cone.Conversely,every amenable partial order on S can be constructed in this way.We give some properties of a locally inverse semigroup with a Clifford transversal.In particular,if S is a locally inverse semigroup with a Clifford transversal,then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S.Let S be a locally inverse semigroup with an inverse transversal S°. In this paper, we construct an amenable partial order on S by an R-cone. Conversely, every amenable partial order on S can be constructed in this way. We give some properties of a locally inverse semigroup with a Clifford transversal. In particular, if S is a locally inverse semigroup with a Clifford transversal, then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S.

关 键 词：locally inverse semigroup inverse transversal amenable partial order orderpreserving bijection. 

分 类 号：O152.7[理学—数学] TP316[理学—基础数学]