29438.三角范疇中presilting子范疇的mutations及其torsionpairs

1、分類(lèi)號(hào)學(xué)校代碼!Q墨鯉學(xué)號(hào)—201102—100929三角范疇中presilting子范疇的mutations及其torsionpairsMutationsandtorsionpairsofthepresilting_‘●●1‘osubcategorieslntriangulatedcategories研究生姓名墮墊墊指導(dǎo)教師姓名、職稱(chēng)歐陽(yáng)柏玉教授學(xué)科專(zhuān)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一四年五月ABSTRAC

2、TTorsionpairsandmutationsoftorsionpairsareoneoftheforefronthotissuesaboutalgebrarepresentationintriangulatedcategories，atthesametime，presiltingsubcategorywhichisanewsubcategoryisproposedintriangulatedcategoriesInthisthes

3、is，wearemainlyfocusedonresearchingmutationsandtorsionpairsofthepresiltingsubcategoriesThismaster’SdegreethesisconsistsofthreechaptersInfirstchapter，weintroducesomebasicdefinitions，backgroundsneededinthesequelandthemainre

4、sultsofthisthesisInsecondchapter，firstlywepresenttheconceptsofsilting，presilting，partialsiltingsubcategoryandtherelationsbetweenthemSecondlywegivesomedefinitionsandresultsofnewsubcategoryaboutthepresiltingsubcategoryThir

5、dlyweintroducethedefinitionof／9一presiltingmutationFinallywegivethedefinitionsofpresiltingmutationsandequivalentcharacterizationsbetweenthemMeanwhile，westudysomeresultsaboutpresiltingmutationsInthirdchapter，weprovidesomec

6、onceptsandpropertiesabouttorsionpairsandthedefinitionsofpresiltingtorsionpairsandmaximalpresiltingtorsionpairsFinally，wegivethetransformationsbetweenthemandtheir爭(zhēng)quivalentcharacterizationsKeywords：presiltingsubcategories