Filtering modules of finite projective dimension
2003; De Gruyter; Volume: 15; Issue: 3 Linguagem: Inglês
10.1515/form.2003.020
ISSN1435-5337
AutoresHenning Krause, Øyvind Solberg,
Tópico(s)Nonlinear Waves and Solitons
ResumoAbstract.ForarightartinianringL weshowthatforeverynb0thereexistsapure-injectiveL-moduleP n suchthattheL-modulesofprojectivedimensionatmostnarepreciselythedi-rectfactorsofL-moduleshavingafinitefiltrationinproductsofcopiesofP n .Thisisaconse-quence of a general description of certain contravariantly finite resolving subcategories ofModL.Itleadsinadditiontoaone-to-onecorrespondencebetweenequivalenceclassesof(notnecessarilyfinitelygenerated)cotiltingmodulesandresolvingsubcategoriesofModL whichareclosedunderproductsandadmitfiniteresolutionsandspecialrightapproximations.Asanapplicationitisshownthateveryfinitelypresentedpartialcotiltingmoduleoveranartinalgebraadmitsacomplement.2000MathematicsSubjectClassification:16E10;16G10,18G25. 1 IntroductionLet L be a ring (associative with 1) and consider the category ModL of (left)L-modules. In this paper we study the modules of finite projective dimension andprovethefollowingresult.Theorem1.LetL bearightartinianring.Thenthereexistsforeveryintegernb0apure-injectiveL-moduleP
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