| 具有逆断面的局部逆半群 |
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| 引用本文： | 邵勇,赵宪钟.具有逆断面的局部逆半群[J].数学研究及应用,2009,29(4):599-606. |
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| 作者姓名： | 邵勇 赵宪钟 |
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| 作者单位： | 西北大学数学系, 陕西 西安 710127;西北大学数学系, 陕西 西安 710127; 江西师范大学数学与信息科学学院, 江西 南昌 330022 |
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| 基金项目： | 国家自然科学基金(No.10471112); 陕西省教育厅自然科学专项基金(No.07JK413). |
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| 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.
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| 关 键 词： | 逆半群 逆断面 命令 偏序 |
| 收稿时间： | 9/8/2007 12:00:00 AM |
| 修稿时间： | 1/4/2008 12:00:00 AM |
Locally Inverse Semigroups with Inverse Transversals |
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| SHAO Yong and ZHAO Xian Zhong.Locally Inverse Semigroups with Inverse Transversals[J].Journal of Mathematical Research with Applications,2009,29(4):599-606. |
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| Authors: | SHAO Yong and ZHAO Xian Zhong |
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| Institution: | 1. Department of Mathematics, Northwest University, Shaanxi 710127, China
2. Department of Mathematics, Northwest University, Shaanxi 710127, China;College of Mathematics and Information Science, Jiangxi Normal University, Jiangxi 330022, China |
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| Abstract: | Let $S$ be a locally inverse semigroup with an inverse transversal $S^{\circ}$. 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 $S$. |
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| Keywords: | locally inverse semigroup inverse transversal amenable partial order order-preserving bijection |
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