三角范疇中的余撓偶.pdf

1、學(xué)校代碼!Q絲至三角范疇中的余撓偶Thecotorsionpairsintriangulatedcategories研究生姓名李彩瓊指導(dǎo)教師姓名、職稱張衛(wèi)副教授學(xué)科專業(yè)基礎(chǔ)數(shù)學(xué)研究方向’代數(shù)學(xué)湖南師范大學(xué)學(xué)位評(píng)定委員會(huì)辦公室二O一三年五月ABSTRACTThetriangulatedcategoryisintroducedbyGrothendieckinthesixtiesInthepastdecades，Verdierhasdevel

2、opedthetheoryandapplicationofthetriangulatedcategorygreatlybecominggraduallyaDimportantresearchdirectionofalgebraandgeometryOnonehand，thetwoimportantbranches，derivedcategoryandhomologicalalgebra，havebeendevelopedtoanadva

3、ncedlevel；Ontheotherhand，inthetriangulatedcategorytorsionpairsandc伊torsionpairshavebecomefundamentalinalgebraTorsionpairsareexploredindepthbymanywritersForthedual，wecandeducemanysimilarlybutdiscriminatingproperties，andth

4、en，getsomeespecialpropertiesofcotorsionpairsMoreover，wecandescribetherelationshipsbetween’torsionpairsandcotorsionpairstoseveralaspectsWearegoingtoprovidequotientcategoriesfromatriangulatedcategoryviathecoreofcotorsionpa

5、irsThenunderthespecialconditions，thereinduceabelcategoryThisthesisconsistsoffourchaptersInchapterone，weintroducesomenotionsandsigns，inducetheconceptoftorsionpairsandbackgroundsneededinthesequelInchaptertwo，firstlywegivet

6、hedeftnitionofcotorsionpairs，andintroducetherelationshipsbetweentorsionpairsandcotorsionpairsThenweinducesomepropertiesofcotorsionpairsviathepropertiesoftorsionpairsInchapterthree，wegivethedefinitionofcoreofcotorsionpair

7、s，andintroducetherelationshipsofthemThenweinducesomeconclusionstakingadvantageoftheconclusionsinchaptertwoThereprovidequotientcategoriesfromtriangulatedcategoriesviathecoreofcotorsionpairsThengivethepropertiesofthemorphi

8、sminquotientcategories，andgettheimportanttheoremneededinnextchapterInthecomingchapterfour，wegivethedefinitionofabelcategoryThenweproofthatthequotientcategoryunderthespecialconditionsisabelcategoryviatheconclusionsbeforeG