关于弱p-反演半群若干的研究

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6、P-0,E-u℄ail_T6℄"℄<>SOMESTUDIESONWEAKLYP-INVERSIVESEMIGROUPSABSTRACTInthispaper,westudyweaklyP-inversivesemigroups.Itiscomposedoffourchapters.Chapter1isabriefintroductionandthebasicconceptsandnecessaryprelim-inaries.WeintroduceconceptsofweaklyP-i

7、nversivesemigroupsandthestrongP-congruences.Inchapter2,weprovethatthelatticeofstrongP-congruencesisacompletesublatticeofthelatticeofcongruences.Atthesametime,theleastelementofthelatticeofstrongP-congruencesisgiven.Furthermore,wediscusstherelationsbet

8、weenstrongP-congruencesonweaklyP-inversivesemigroupsandregular∗-semigroups.Inchapter3,weintroduceconceptsofstrongnormalpartition,strongnor-malequivalenceandtheconceptofcharacteristictraceofstrongP-congruencesonP-inversivesemigroups.Byusingthem,westud

9、ythepropertiesofthelatticesofstrongP-congruences,suchasthegreatestelementrespecttohavingstrongnormalequivalenceasitsC-trace,relationθdeterminedbystrongnormalequiv-alenceisacongruenceonlatticesofstrongP-congruencesandeachθ-classisacompletesublatticeof

10、latticesofstrongP-congruencesandsoon.Inchapter4,wegivetheconstructionofallP-subdirectproductsofweaklyP-inversivesemigroupsandweintroducetheconceptsofE-unitaryweaklyP-inversivecoversofweaklyP-inversivesemigroupsandstudytheunitaryP-subho-momorphismsofw