秦美青

（菏澤學(xué)院 數(shù)學(xué)系，山東 菏澤 274015）

有限保E-序部分變換半群的變種半群上的格林關(guān)系

秦美青

（菏澤學(xué)院 數(shù)學(xué)系，山東 菏澤 274015）

設(shè)X是一個(gè)有限全序集，E是集合X上的等價(jià)關(guān)系.令PEOPX={α∈PX∶?x,y∈domα,(x ,y)∈E且x≤y?(xα ,yα )∈E且xα≤yα} ，取定 θ∈PEOPX，在PEOPX上定義一個(gè)運(yùn)算“o”，其中α°β=αθβ，得到一個(gè)新的半群稱為保E-序部分變換半群的變種半群，記為PEOPX(θ).本文主要刻劃半群 PEOPX(θ)上的格林關(guān)系.

部分變換半群；保E-序部分變換半群；變種半群；格林關(guān)系

1 引言與預(yù)備知識(shí)

2 主要結(jié)果

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Green’s Relations for the Variants of Finite E-Order-preserving Partial Transformations Semigroups

QIN Meiqing
（Department of Mathematics，Heze University，He ze274015，China）

LetXbe a finite totally ordered set andEbe an equivalence onX.DenotePEOPX={α∈PX∶?x,y∈doma,(x ,y)∈E且x≤y?(xα ,yα )∈E且xα≤yα} .Fix an elementθand define an operation onPEOPXby α°β=αθβ andPEOPXforms a semigroup which is called the variant semigroup of finite E-Order-preserving partial transfor?mations semigroups,and it was denoted asPEOPX(θ).In this paper,we describe the Green’s relation for the semi?groupPEOPX(θ).

partial transformation semigroup；E-Order-preserving partial transformations semigroups；Green’s relation

O 152.7

A

1674-4942（2011）01-0006-03

2010-11-16

畢和平