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  5. Άρθρα σε επιστημονικά περιοδικά ( Ανοικτά). ΜΑΘ
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Please use this identifier to cite or link to this item: https://olympias.lib.uoi.gr/jspui/handle/123456789/12911
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dc.contributor.authorBeligiannis, A.en
dc.contributor.authorReiten, I.en
dc.date.accessioned2015-11-24T17:24:32Z-
dc.date.available2015-11-24T17:24:32Z-
dc.identifier.issn0065-9266-
dc.identifier.urihttps://olympias.lib.uoi.gr/jspui/handle/123456789/12911-
dc.rightsDefault Licence-
dc.subjecttorsion pairsen
dc.subjectcotorsion pairsen
dc.subjectabelian categoriesen
dc.subjectt-structuresen
dc.subjecttriangulated categoriesen
dc.subjectcompact objectsen
dc.subjecttilting theoryen
dc.subjectderived categoriesen
dc.subjectcontravariantly finite subcategoriesen
dc.subjectapproximationsen
dc.subjectstable categoriesen
dc.subjectreflective subcategoriesen
dc.subjectresolving subcategoriesen
dc.subjectclosed model structuresen
dc.subjectcohen-macaulay modulesen
dc.subjecttate-vogel cohomologyen
dc.subjectgorenstein ringsen
dc.subjectcontravariantly finite subcategoriesen
dc.subjectauslander-reiten trianglesen
dc.subjectstable equivalenceen
dc.subjectabelian categoriesen
dc.subjecttriangulated categoriesen
dc.subjectrepresentation-theoryen
dc.subjectgorenstein algebrasen
dc.subjectrelative homologyen
dc.subjecttate cohomologyen
dc.subjecttilting modulesen
dc.titleHomological and homotopical aspects of torsion theories - Introductionen
heal.typejournalArticle-
heal.type.enJournal articleen
heal.type.elΆρθρο Περιοδικούel
heal.identifier.secondary<Go to ISI>://000247277400001-
heal.languageen-
heal.accesscampus-
heal.recordProviderΠανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικώνel
heal.publicationDate2007-
heal.abstractIn this paper we investigate homological and homotopical aspects of a concept of torsion which is general enough to cover torsion and cotorsion pairs in abelian categories, t-structures and recollements in triangulated categories, and torsion pairs in stable categories. The proper conceptual framework for this study is the general setting of pretriangulated categories, an omnipresent class of additive categories which includes abelian, triangulated, stable, and more generally (homotopy categories of) closed model categories in the sense of Quillen, as special cases. The main focus of our study is on the investigation of the strong connections and the interplay between (co)torsion pairs and tilting theory in abelian, triangulated and stable categories on one hand, and universal cohomology theories induced by torsion pairs on the other hand. These new universal cohomology theories provide a natural generalization of the Tate-Vogel (co)homology theory. We also study the connections betweeen torsion theories and closed model structures, which allow us to classify all cotorsion pairs in an abelian category and all torsion pairs in a stable category, in homotopical terms. For instance we obtain a classification of (co)tilting modules along these lines. Finally we give torsion theoretic applications to the structure of Gorenstein and Cohen-Ma,caulay categories, which provide a natural generalization of Gorenstein and Cohen-Macaulay rings.en
heal.publisherAmerican Mathematical Societyen
heal.journalNameMemoirs of the American Mathematical Societyen
heal.journalTypepeer reviewed-
heal.fullTextAvailabilityTRUE-
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