對合Quantale及其范疇性質(zhì).pdf

1、陜西師范大學碩士學位論文對合Quantale及其范疇性質(zhì)姓名：肖瀅申請學位級別：碩士專業(yè)：基礎(chǔ)數(shù)學指導教師：趙彬20050401InvolutiveQuantaleandItsCategoricalPropertiesXIAOYingAbstract：SincetheconceptofquantalewasintroducedbyCJMulveyin1986，manymathematiciansandlogicistspayclosea

2、ttentiontothetheoryofquan—talesBasingOilthetheoryofquantalesandthetheoryoftalgebras，CJMulveyandJWPelletieradvancedanewconcept一一involutivequantale，in1992TheaimofthispaperistostudysomebasicpropertiesofinvolutivequantalesAc

3、cordingtotheresearchesconcerningthecongruencerelationandthehomomorphismofinvolutivequantales，wecandiscusstheliftonpowerinvolutivequantalesfurtherAtlast，wealsostudycarefullyanddeeplythelimitandtheinverselimitofthecategory

4、ofinvolutivequantalesThearrangementofthispaperisasfollows：ChapterOneP他liminaryknowledgeInthischapter，wegivethebasicconceptsandresultsofthetheoryofquantalesandthetheoryofcategorywhichareusedinthewholepaperChapterTwoInvolu

5、tiveQuantalesInthispart，somebasicconceptsofin—volutivequantalesaredefined，suchasinvolutivequantales，homomorphisms，sub—involutivequantales，ideals，nucleisandsomespecialelementsofaninvolutivequan—tale。Meanwhile，wewouldliket

6、ogivesortieexamplesofinvolutivequantalesanddiscussafewpropertiesaboutinvoltionsThen，westudysomepropertiesaboutsub—involutivequantalesandidealsofinvolutivequantales，andconstructsometypesofthemChaperThreeTheCongruenceRelat

7、ionolanInvolutiveQuantaleFirstlywegivethedefinitiouofthecongruencerelationofaninvolutivequantaleandargueabouttherelationshipbetweenthecongruencerelationandthehomomorphismSecondly，wegiveanequivalentitemthatanequivalentrel

8、ationonaninvolutivequantaleisacongruencerelationThen，wealsodiscussthecongruencerelationontheproductofinvolutivequantalesandakindofcongruencerelationwhichisinducedbyanidealofaninvolutivequantaleAndthen，inviewofthedefiniti