雙半環(huán)的結(jié)構(gòu)和同余.pdf

1、江西師范大學(xué)碩士學(xué)位論文雙半環(huán)的結(jié)構(gòu)和同余姓名：張偉申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：王頌生20070501ABSTRACTInthisdissertation，wegiveacharacterizationofthebisemiringcongruencesanddiscussthreeGreenrelationsontheidempotentbisemiringThenwestudysomestructuresofbisem

2、iringsthroughsomebisemiringcongruencesThemainresultsaregivenasfollows：InChapter1，wegivetheintroductionandpreliminariesInChapter2，wemainlygiveacharacterizationofbisemiringcongruencesandgettheleastbiringcongruenceandthelea

3、stadditiveinversebisemiringcongruenceonsomebisemiringsinthefirstsectionInotherthreesectionswestudytheGreen9：relation，Green舅relationandGreenSrelation，andgetthenecessaryandSUfficient^●‘‘十‘^t‘conditionsofDnDnDRf1RnRandLnLnL

4、relationssatisfiedbyelementsoftheidempotentbisemiringsWecharacterizethemasthecongruencesontheidempotentbisemiringsFinallywegettheMal’cevproductdecompositionofthecorrespondingsubvarietiesInChapter3，wemainlystudythepseudos

5、trongdistributivelatticeofbisemiringvarietiesandgetthepseudosubdirectproductdecompositioninthefirstsectionInthesecondsectionwedisCUSSthestructureoftheadditionIeftnormalbisemiringswhichsatisfiestheidentities口aba—aand口ban=

6、口AndwehavethedirectproductdecompositionofsomebisemiringInChapter4thepseudo—strongsemilatticeofthebisemiringvarietiesiSstudiedWediscussthestructureofthemultiplicationnormalbisemiring，whichsatisfiestheidentitiesababab=口ban

7、daba十bab=a；hbinthefirstsectionAndinthesccondsectionwediscussthestructureofthemultiplicationleftnormalbisemiringssatisfyingtheidentities066口，口bandabba=a#bBasedonthemwefurthergetthedirectproductdecompositionoftwokindsofbis

8、emiringsKeywords：bisemiringcongruence；theidempotentbisemiring；Greenrelation；pseudostrongdistributivelatticeofbisemiringvarieties；pseudo—strongsemilatticeofbisemiringvarieties；theadditionleftnormalbiscmiring；themultiplica