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Vietnam Journal of Mathematics 33:3 (2005) 253-260  Regularity and Isomorphism Theorems of Generalized Order-Preserving Transformation Semigroups Yupaporn Kemprasit and Sawian Jaidee Abstract.  The full order-preserving transformation semigroup $OT(X)$ on a poset $X$ has long been studied. In this paper, we study the semigroup $(OT(X,Y), \theta)$ where $X$ and $Y$ are chains, $OT(X,Y)$ is the set of all order-preserving maps from $X$ into $Y$, $\theta \in OT(Y,X)$ and the operation $*$ is defined by $\alpha * \beta =\alpha \theta \beta$ for all $\alpha , \beta \in OT(X,Y)$. We characterize when $(OT(X,Y), \theta)$ is regular, $(OT(X,Y), \theta)$ $\cong OT(X)$ and $(OT(X,Y), \theta)\cong OT(Y)$.

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