OT(X,Y;θ)的正则元、幂等元的一些特殊性质

Regulations and idempotent properties for finite ordered-preserving sandwich semigroup OT(X,Y;θ)

设X,Y任意的非空全序集合,OT(X,Y)是X到Y的全体保序映射构成的集合,θ是Y到X的一个确定的保序映射.α,β∈OT(X,Y)定义:α°β=αθβ,这里αθβ表示一般映射的合成,则OT(X,Y)关于运算构成一个半群,称为保序的夹心半群,记为OT(X,Y;θ).当X,Y都是有限集合且X>1,Y>1时称保序夹心半群OT(X,Y;θ)为有限保序夹心半群.主要讨论有限保序夹心半群正则元、幂等元的一些特殊性质.

Let X and Y be arbitrary nonempty order sets, OT（X, Y） be the set of mappings from X to Y, θ be ar- bitrary but fixed mapping from Y to X for any V a,BE OT（X, Y） , the operation in OT（ X, Y） is defined by a~/3 = a0/3 ,where a0/3 is the production of mappings. Then OT（X, Y） forms a semigroup called sandwich semigroup and de- noted by OT（X, Y） . The sandwich semigroup OT（ X, Y） is called finite preserving order sandwich semigroup when both X and Y are finite sets and { X } 〉 1, { Y } 〉 1. In this paper, we discuss the regulations and idempotent proper- ties of OT（ X, Y;θ）