正則半群的雙序集表示及應(yīng)用.pdf

1、四川師范大學(xué)碩士學(xué)位論文正則半群的雙序集表示及應(yīng)用姓名：徐芒申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：喻秉鈞2002.3.30AbstractSincethealgebraictheoryofsemigroupswasindependentofotherbranchesofalgebram60，sof20thcentury，thestudyofpropertiesandstructuresofvariousclassesofregula

2、rsemigroupshasbeenthedominatingaspectinthetheoryandresultedtoaquiteabundantandcompletesubject，thetheoryofregularsemigroupsInthetheoryofregularsemigroups，aconstructivetheorem，duetoWDMunn，forinversesemigroupsandastructural

3、theorem，duetoTEHall，fororthodoxsemigroupsestablishedtwoimportantmilestonesinthedevelopmentofthestudyTheygaveconcreteconstructionsofafundamentalinversesemigroupTE(theMunn’ssemigroupofthesemilatticeE)andafundamentalorthodo

4、xsemigroupWs(theHall’SsemigroupofthebandB)intermsofisomorphismsbetweenprincipalidealsinasemilatticeEorbandBrespectivelyOnthebasisofthesetwoconstructions，MunnandHallgavefundamentalrepresentationsforthesetwoclassesofregula

5、rsemigroupsAsforconstructionofreghlarsemigroupsingeneraljafamousIndiamathematicianKSS，Nambooripadinitiatedthetheoryofregularbiorderedsetsandsolvedinglobalthestructureofarbitraryregularsemigroupsbyusingequivalenceofcatego

6、riesInthefirsttWOsectionsofthisthesis，byusingisomorphismsbetweenprincipalidealinanarbitraryregularbiorderedsetE，wegiveaconcreteconstructionofafundamentalregularsemigroupWE(namedNHsemigroupofbiorderedsetE)Onthebasisofthis

7、constructionwegiveafllndamentalrepresentationforarbitraryregularsemigroupsfseeTheorem221)Inparticular，whenEisasemilatticeorbandbiorderedset，ourWEisexactlyisomorphictotheMunnlSsemigroupTEortheHall’SsemigroupWs(E(B)蘭E)resp

8、ectivelyThusourworkgeneralizesbothrepresentationtheoriesduetoWDMunnandTEHallforinverseandorthodoxsenligroupstogeneralregularsemigroupsTheconceptofweaklyinversesemigroupwasintroducedbyanotherIndianmathematicianBR，Srinivas

9、anin1968asageneralizationofinversesemigroupsHeprovedthatthesetWT(A)ofallpartialtransformationsonanarbitrarysetAformsaweaklyinversesemigroup，calledthesymmetricweaklyinversesenfigroup，andthatanyweaklyinversesemigroupScanbe

10、embeddedintothesymmetricweaklyinversesemigroupP丁(S)In1976，KSS，Nambooripadgeneralizedthisconcepttothatof(LR)semigroupandgaveasufficientandnecessaryconditionsforan(LR)semigrouptobeweaklyinversesemigroupIn1999，YUShi—weietc，

11、provedthatanyidempotent—separatinghomomorphicimageofthesymmetryweaklyinversesemigroupisstillweaklyinverseButtheproblemwhetherornotidempotent—separatinghomomorphicimagesofanarbitraryweaklyinversesemigrouparealsoweaklyinve