型A半群的某些分析

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1、SomeResearchAboutType-ASemigroupsBasicMathematicsWriter：GuoQianSupervisor：YuBingjunAbstract：Inthisthesis，byusingofthecommutativityofidempotentsitheidempotent—connection，thecompatibilityofthenaturalpartialorderwithre-specttothemultiplicationandtheclosureinatypeAsemigroupaswellasthelocalizationtheory

2、oftypeAsemigroups，weinvestigatethefoHowingfourbasicquestions：1．characterizationoftheVagner-Prestonrepresentationofatype-Asemi—group；2．characterizationoftheSchfitzenbergerrepresentationofatype-Asemi-group；3．characterizationofrightw-cosetrepresentationonaclosed+一subsemi-groupofatypeAsemigroup；4．chara

3、cterizationoflocalizationofatype-Asemigrouponitssubsemi-groups(inparticular，onitsidempotentsemilattice)．Thethesisisdividedintothreechapters．Inthefirstchapter，wegivesomebasicconceptsoftheGreen’S*-equivalencesandtheirimportantpropertiesrelatedtotheidempotentssuchasabundance，thecommutativityofidempote

4、ntsandtheidempotentJ-connection，andthenatu-ralpartialorderonabundantsemigroupsand，anditscompatibilitywithrespecttothemultiplicationonthesemigroups，SOon，whichareusefulforthethesis．Inthesecondchapter，wediscussthreekindsofrepresentationsfortype-Asemigroups：theVagner-Prestonrepresentation，theSchfitzenb

5、ergerrepresen-rationandtherepresentationOnu—cosetsofclosed+一subsemigroups．The第iii页Vagner-Prestonrepresentation西isageneralizationoftheclassicalCayleyrep-resentationofgroupstoinversesemigroups，wegeneralizefurtherittotype—Asemigroups．Wealsogiveallexampletoshowthat，intheclassofabundantsemigroupsitefl$1

6、notbegeneralizedanymore；TheSchfitzenbergerrepresen-tation113]占isdeftnedbasedonthepropertiesofGreen’srelations冗andc．UsingtheGreen’S+relation冗+．wegeneralizeittotypeAsemigroups．Weprovethat西￡Jandgiveanexampletoshowthattheconclusionisgenerallyproper．Itisawell-knownclassicalresultthattherepresentationofa

7、grouponthecosetsofitssubgroupiseffectiveandtransitive．ThisclassicalresultwasgeneralizedtoinversesemigroupsbyfamousSovietmathematicianB．M．Scheinin1962(see，1141)．Inthischapter，bygeneralizingtheconceptoftransi