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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.
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