羅永貴

(貴州師范大學(xué) 數(shù)學(xué)與計算機科學(xué)學(xué)院，貴州 貴陽 550001)

羅永貴

(貴州師范大學(xué) 數(shù)學(xué)與計算機科學(xué)學(xué)院，貴州 貴陽 550001)

保序；壓縮；降序；奇異變換半群；相關(guān)秩

1 預(yù)備知識

其中，每個Ai(i∈[1，k])都是[n]的凸子集，Aiα=i,i≤minAi，A1

(α,β)∈L*?Imα=Imβ,(α,β)∈R*?Kerα=Kerβ，(α,β)∈J*?|Imα|=|Imβ|．

本文未定義的術(shù)語及符號參見文獻(xiàn)[11-13]．

2 定理的證明

為完成定理的證明先給出若干引理與推論．

令

其中，每個Ai(i∈[1,k])都是[n]的凸子集，Aiα=i,i≤minAi，A1

令

定理的證明

當(dāng)1≤l

[1]徐 波，馮榮權(quán)，高榮海．一類變換半群的秩[J]．?dāng)?shù)學(xué)的實踐與認(rèn)識，2010，40(8)：222～224．

[2]高榮海，徐 波．關(guān)于保序壓縮奇異變換半群的秩[J]．山東大學(xué)學(xué)報(理學(xué)版)，2011，46(6)：4～7．

[3]李俊揚．一類降序變換半群的秩[J]．貴州師范大學(xué)學(xué)報(自然科學(xué)版)，2012，30(4)：69～70，120．

[4]G.M.S.Gomes,J.M.Howie.On the Ranks of Certain Semigroups of Order-Preserving Transformations[J]．Semigroup Forum,1992,45(1):272～282．

[5]G.U.Garba.On the Idempotent Ranks of Certain Semigroups of Order-Preserving Transformations[J]．Portugaliae Mathematica,1994,51(2):185～204.

[6]A.Umar.On the Semigroups of Order-Decreasing Finite Full Transformations[J]．Proceedings of the Royal Society of Edinburgh:Sect A Math,1992,120:129～142．

[7]A.Umar.On the Ranks of Certain Finite Semigroups of Order-Decreasing Transformations[J]．Portugaliae Mathematica,1996,53(1):23～34.

[8]A.Laradji,A.Umar.On certain finite semigroups of order-decreasing transformations[J]．Semigroup Forum,2004,69(2):184～200.

[9]J.M.Howie,N.Ruskuc,P.M.Higgins.On Relative Ranks of Full Transformation Semigroups[J]．Communication in Algebra,1998,26(3):733～748.

[10]J.B.Fountain.Abundant Semigroups[J]．Proc London Math soc,1982,44(3):103～129．

[11]J.M.Howie.Fundamentals of Semigroup Theory[M]．Oxford:Oxford University Press,1995.

[12]O.Ganyushkin,V.Mazorchuk.Classical Finite Transformation Semigroups[M]．London:Springer-Verlag,2009．

[13]N.Ruskuc.Semigroup Presentations[D]．St Andrews:university of St Andrews,1995.

LUOYong-gui

(Department of Mathematics and Computer Science,Guizhou Normal University,Guiyang 550001,Guizhou)

LetWbe the semigroup of all order-preserving and compressing singular transformations with decreasing on a finite-chain[n] ifn≥3,and letK(n,r)={α∈W：|Imα|≤r}be the two-sided star ideal of the semigroupsWfor an arbitrary integerrif 1≤r≤n-1．By analyzing the elements of rankrand star Green's relations,the relative rank of the semigroupsK(n,r) with respect to itself each star idealK(n,r) is determined if 1≤l

order-preserving;compression;decreasing;singular transformation semigroup;relative rank

梁懷學(xué))

2014-05-21

貴州省科學(xué)技術(shù)基金資助項目(黔科合J字LKS(2013)01號)

羅永貴(1985-)，男，苗族，貴州省安順市人，現(xiàn)為貴州師范大學(xué)數(shù)學(xué)與計算機科學(xué)學(xué)院講師.研究方向：半群代數(shù)理論.

O152.7

A

1674-3873-(2014)03-0087-03