關(guān)于余代數(shù)的結(jié)構(gòu)與表示.pdf

1、北京工業(yè)大學(xué)碩士學(xué)位論文關(guān)于余代數(shù)的結(jié)構(gòu)與表示姓名：曹貽鵬申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：姚海樓20080401北京工業(yè)大學(xué)理學(xué)碩士學(xué)位論文AbstractIn1945MacLaneandEilenbergintroducedtheconceptandtheoriesofcategories，whichhaveplayedaroleinmanybranchesofmathematicssuchasalgebraicgeomet

2、ry，topology，differentialgeometryandfunctionaltheoryTherepresentationtheoryofalgebraswasdevelopedin1970s，whichisanimportantbranchofmathematicsTherepresentationtheoryisasubjectinwhichonemostlystudiesthestructuresoffinitely

3、dimensionalalgebras，indecomposablerepresentationsandglobalconstructionofmodulecategoriesCoalgebrasaredefinedbywayofdualizingalgebrasOnthebaseofresearchingmodulecategoriesofalgebras，studyingcomodulecategoriesofcoalgebrasi

4、simportantfordiscussingstructuresandrepresentationsofcoalgebrasThisthesismainlycontainsthefollowingcontentsInChapterone，wegivesomenotations，basicconcepts，researchingbackgroundandthemainresultsInchaptertwowediscussthehomo

5、logyproperties，mainlydiscussthehomologypropertiesofbasiccoalgebrasandhereditarycoalgebras，andtheapplicationofchangesofcoalgebraappliedinthetwocoalgebrasInchapterthreewediscusstheCO—frobeniuscoalgebrawhichisonekindofimpor

6、tantsemi—perfectcoalgebrasInparticular，weresearchthemaximalrationalsubmodules，denseproperties，torsionratfunctorandthedirectsumtensorofCO—frobeniuscoalgebrasInchapterfour，wediscussserialcoalgebraswhichhavespecialstructure