Tilting objects in abelian categories and quasitilted rings

DOI10.1090/S0002-9947-06-03909-2zbMath1111.16008OpenAlexW1574577152WikidataQ61795032 ScholiaQ61795032MaRDI QIDQ3420289

Kent R. Fuller, Riccardo Colpi

Publication date: 1 February 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-06-03909-2

zbMATH Keywords

endomorphism ringsAbelian categoriesquasitilted algebrastilting objectsquasitilted rings

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Module categories in associative algebras (16D90) Torsion theories, radicals (18E40) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Torsion theories; radicals on module categories (associative algebraic aspects) (16S90) Homological dimension in associative algebras (16E10)

Related Items (16)

The HRS tilting process and Grothendieck hearts of t-structures ⋮ Cotorsion pairs, torsion pairs, and \(\varSigma \)-pure-injective cotilting modules ⋮ THE YONEDA EXT AND ARBITRARY COPRODUCTS IN ABELIAN CATEGORIES ⋮ On the heart of a faithful torsion theory ⋮ Derived, coderived, and contraderived categories of locally presentable abelian categories ⋮ On tilted Giraud subcategories ⋮ Tilting subcategories in extriangulated categories ⋮ Localizations, colocalizations and non additive \(\ast\)-objects ⋮ Stability approach to torsion pairs on abelian categories ⋮ Cotilting sheaves on Noetherian schemes ⋮ When the heart of a faithful torsion pair is a module category ⋮ Perverse coherent t-structures through torsion theories ⋮ Large tilting sheaves over weighted noncommutative regular projective curves ⋮ Tilting and cotilting modules over concealed canonical algebras ⋮ Tilting via torsion pairs and almost hereditary Noetherian rings. ⋮ Semidualizing and tilting adjoint pairs, applications to comodules.

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