| Green's Relations on Semigroups of Transformations Preserving Two Equivalence Relations |
| Received:March 31, 2007 Revised:October 06, 2008 |
| Key Words:
transformation semigroup equivalence regular element Green's relations.
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| Fund Project:the Natural Science Found of Henan Province (No.0511010200); the Doctoral Fund of Henan Polytechnic University (No.B2009-56); the Natural Science Research Project for Education Department of Henan Province (No.2009A110007). |
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| Abstract: |
| Let ${\cal T}_X $ be the full transformation semigroup on a set $X$. For a non-trivial equivalence $F$ on $X$, let $T_F (X) =\{ f\in {\cal T}_X : \forall \, (x,y)\in F,\,(f(x),f(y))\in F \}.$ Then $T_F(X) $ is a subsemigroup of ${\cal T}_ X $. Let $E$ be another equivalence on $X$ and $T_{FE}(X)=T_F(X)\cap T_E(X)$. In this paper, under the assumption that the two equivalences $F$ and $E$ are comparable and $E\subseteq F$, we describe the regular elements and characterize Green's relations for the semigroup $T_{FE}(X)$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2009.03.005 |
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