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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), θ) where X and Y are chains, OT(X, Y) is the set of all order-preserving maps from X into Y, θ  OT(Y, X) and the operation * is defined by α * β = αθβ for all α, β  OT(X, Y). We characterize when (OT(X, Y), θ) is regular, (OT(X, Y), θ)  OT(X) and (OT(X, Y), θ)  OT(Y).

 

 

 

 

 

 

 

 

 

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