半群PO(X,Y,θ)的格林关系及正则元

Green's relations and regularity for the semigroup PO( X,Y,θ)

设X和Y是有限非空集合,PO(X,Y)表示从X到Y的所有部分保序映射构成的集合.取定θ∈PO(Y,X),在PO(X,Y)上定义运算,如:αβ=αθβ,则(PO(X,Y),)是一个半群,称为有限部分保序夹心半群,记为PO(X,Y,θ).半群PO(X,Y,θ)的格林关系及其正则元被刻划了.

Let X and Y be nonempty finite set.Let PO （X,Y） be all partial order-preserving mapping from X into Y and let θ∈PO（Y,X）.The operation .is defined by α .β =αθβ,for all α,β∈PO（X,Y）.Then （PO（X,Y）,.） is a semigroup and call order-preserving sandwich semigroups of all finite partial mapping from X into Y and so denote PO（X,Y,θ）.The Green＇s relations and regularity for the semigroup PO（X,Y,θ） are characterized.