| Regularity and Green's Relations on a Special Transformation Semigroup |
| Received:February 15, 2006 Revised:December 12, 2006 |
| Key Words:
transformation semigroup equivalence regular element Green's relations orientation-preserving map.
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| Fund Project:the Natural Science Foundation of Henan Province (0511010200). |
| Author Name | Affiliation | | SUN Lei | School of Sciences, Xi'an Jiaotong University, Shaanxi 710049, China | | PEI Hui-sheng | College of Mathematics and Information Science, Xinyang Normal University, Henan 464000, China
Institute of Mathematics, Henan Computer Center, Henan 450008, China | | CHENG Zheng-xing | School of Sciences, Xi'an Jiaotong University, Shaanxi 710049, China |
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| Abstract: |
| 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 $OP_E(X)$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2007.03.019 |
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