秦美青
(菏泽学院 数学系,山东 菏泽 274015)
有限保E-序部分变换半群的变种半群上的格林关系
秦美青
(菏泽学院 数学系,山东 菏泽 274015)
设X是一个有限全序集,E是集合X上的等价关系.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上定义一个运算“o”,其中α∘β=αθβ,得到一个新的半群称为保E-序部分变换半群的变种半群,记为PEOPX(θ).本文主要刻划半群 PEOPX(θ)上的格林关系.
部分变换半群;保E-序部分变换半群;变种半群;格林关系
[1]刘振玲.几类变换半群的正则性及格林关系[D].山东:山东师范大学,2008.
[2]秦美青.关于几类变换半群的研究[D].山东:山东师范大学,2009.
[3]Pei H S.Green's relations for the variants of transforma⁃tion semigroups preserving an equivalence relation[J].Communications in Algebra,2007,35:171-1986.
[4]Pei H S.Semigroups of partial transformations preserving an equivalence relation[J].数学进展,2009,38(1):103-118.
[5]Pei H S.Regularity and Green s relations for semigroups of ransformations that preserving an equivalence[J].Communications in Algebra,2005,33,108-109.
[6]Howie J M.Fundamentals of Semigroup Theory[M].New York:Oxford University Press,1995.
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
毕和平