OT（X，y；θ））的正则元、幂等元的一些特殊性质

摘要

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，0是Y到X的一个确定的保序映射．Va，B∈OT（X，y）定义：旺B=aθB，这里aθB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；O）．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；O）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)