| 孙垒,裴惠生,程正兴.一类变换半群的正则元和Green关系[J].数学研究及应用,2007,27(3):591~600 |
| 一类变换半群的正则元和Green关系 |
| Regularity and Green's Relations on a Special Transformation Semigroup |
| 投稿时间：2006-02-15 修订日期：2006-12-12 |
| DOI：10.3770/j.issn:1000-341X.2007.03.019 |
| 中文关键词: 变换半群 等价关系 正则元 Green关系 保向映射. |
| 英文关键词:transformation semigroup equivalence regular element Green's relations orientation-preserving map. |
| 基金项目:河南省自然科学基金(0511010200). |
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| 中文摘要: |
| 设${\cal T}_{X}$为$X$上的全变换半群, $E$为$X$上的等价关系. 令$$T_{E}(X)=\{f\in{\cal T}_{X}:\,\forall \, (x, y)\in E,(f(x), f(y))\in E\},$$则$T_{E}(X)$是${\cal T}_{X}$的子半群. 如果$X$是一个全序集, $E$是$X$上的一个凸等价关系,设$OP_E(X)$为$T_{E}(X)$中所有保向映射作成的半群. 对于有限全序集$X$上一类特殊的凸等价关系$E$, 本文刻画了半群$OP_ |
| 英文摘要: |
| Let ${\cal T}_{X}$ be the full transformation semigroup on a set $X$, and $E$ an equivalence on $X$. Let $$T_{E}(X)=\{f\in{\cal T}_{X}:\,\forall \, (x,y)\in E,(f(x),f(y))\in E\}.$$ Then $T_{E}(X)$ forms a subsemigroup of ${\cal T}_{X}$. If $X$ is a totally ordered set and $E$ is a convex equivalence on $X$, then let $OP_{E}(X)$ be a semigroup consisting of all the orientation-preserving maps in $T_{E}(X)$. In this paper, for the special convex equivalence $E$ on a finite totally ordered set $X$, we describe the regular elements and characterize Green's relations on the semigroup $OP_E(X)$. |
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