关于4-循环半群的一个子半群-II.pdfVIP

数 学 杂 志 Vo1．33(2013) J．ofMath．(PRC) NO．6 oN A CERTAIN SUBSEM IGR0UP 0F THE 4一CYCLIC SEM IGR0UP —II SHANG Yu ，WANG Li—min (1．DepartmentofMathem。tics，PuerUniersity，Puer665000，China) (2．SchoolofMathematics，SouthChinaNormnlUniversity，Gu。ngzhou510631，China) Abstract：Inthispaper，weinvestigateasubsemigroup B ofthe4-cyclicsemigroupBw2． BYcalculation，wecharacterizetheGreen’sandgeneralizedGreen’StelationsofB_2．Weshow that B-2isa 一trivial}一bisimpletypeA semigroup． Keywords： typeA semigroup；02一semigroup；4-cyclicsemigroup；Green’Srelation 2010MR SubjectClassification： 20M10 Documentcode： A ArticleID： 0255—7797(2013)06—0983—06 1 Introduction and Prelim inaries ForanysemigroupSweshalldenotebyE(S1thesetofidempotentsofS．LetN。be thesetofnon—negativeintegersandS bean arbitrary semigroupand CIbethebicyclic semigroup，i．e．，C1=N 。×N。underthemultiplication (，)(，8)=(i—J+max{j，)，8一k+ma~{j，)) ConsiderW ：C1×swithmultiplicationgivenby((m，n)，s)((p，g)，t)=((m，n)(p，g)，f(n，p)) wheref(n，P)=8，t，orstaccordingtowhethernP，nP，orn=Pandwherejuxtaposi— tiondenotesmultiplicationinCIandS．WarnewroteW = C1oSanddefinedC2= C1。c1 andcalledC2the4-cyclicsemigroupin[1]． In [2】，weintroducethe 。一chain 2，i．e．， 2= N。×N。withorderdefinedby (m，n) (p，q)ifandonlyifmP，orm =Pandn q．Noticingthatif(m，n) (P，q) then m P．W eshow thattheM unn semigroup ofthe 一chain 2 isthe semigroup Ⅳ0×N0×N0×N 0wherethemultiplication iS c，礼，口，pcn，b，d，c= (m,n-q+max{q,6)，d一6+max{g，6)，c)’ f；p；=三兰a,， Received date：2012—02-27 Accepted date：2012—06-22 Foundationitem：SupportedbytheNationalNaturalScienceFoundationofChina； theScienceFoundationoftheDepartmentofEducationofYunnanProvince(2011Y478)． Biography：Shang