具有純正斷面的正則半群.pdf

1、曲阜師范大學碩士學位論文具有純正斷面的正則半群姓名：孔祥軍申請學位級別：碩士專業(yè)：基礎數學指導教師：鄭恒武20040406AbstractThisdissertationconsistsoffivesectionsWeinvestigateregularsemi—groupswithorthodoxtransversalsThefirstandsecondsectionsareintroductionandpreliminariesre

2、spectivelyThethirdandforthsectionsaredevotedtotheinvestigationoftherelationshipbetweenthequasi—idealorthodoxtransversalsofaregularsemigroupandsomepropertiesofsometypesoforthodoxtransversalsTheconceptoforthodoxtransversal

3、Wasfirstintroducedin[13]ThisisaninterestinggeneralizationofinversetransversalAsforinversetransversalssomeimportantpropertiesonregularsemi—groupswithquasi—idealinversetransversalswereobtained[20，22，23]Asfororthodoxtransve

4、rsal，thequasi—idealorthodoxtransversalsofaregu—larsemigrouparenotnecessarilyisomorphiclbuttheproductofanytwoquasi—idealorthodoxtransversalsofaregularsemigroupSisaquasi—idealorthodoxtransversalofSisobtainedinthisdissertat

5、ionThusthepropertiesonorthodoxtransversalsaredifferentfromthecorrespondingresultsOilinversetransversalsAnumberoftypesoforthodoxtransversalsaregroupedtogetherinsection4，itspropertiesaresimilartothecorrespondingresultsonin

6、versetransversalsForexample，anorthodoxtransversalismultiplicativeifandonlyifitisweaklymultiplicativeandaquasi—idealE—orthodoxtransversalisspecialinterestingLetS。beanE—orthodoxtransversalofaregularsemigroupSThenforanyidem

7、potenteinS，theinversesofeinSoareidempotentsandSoisweaklymultiplicative；Letbetheidempotent—generatedregularsubsemigroupofSThen=z∈S：％。(z)妄E(S。))；AregularsemigroupSwithanor—thodoxtransversalSoisorthodoxifandonlyifSoisEortho

8、doxtransver—salofSandShasaconditionconcerningidempotentThefifthsectionisdevotedtothestructuretheoremofregularsemigroupswithquasi—idealorthodoxtransversalsSomeresultsoninversetransversalsaregeneralizedtoorthodoxtransversa