Cotorsion pairs, torsion pairs, and \(\varSigma \)-pure-injective cotilting modules

DOI10.1016/j.jpaa.2009.06.003zbMath1197.18006arXiv0806.4345OpenAlexW2002248774WikidataQ114155510 ScholiaQ114155510MaRDI QIDQ847139

Riccardo Colpi, Francesca Mantese, Alberto Tonolo

Publication date: 12 February 2010

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.4345

zbMATH Keywords

injective dimensionGrothendieck categoryNoetherian ringcotorsion pairtorsion paircotilting module\(\Sigma\)-pure-injective module

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Torsion theories, radicals (18E40) Abelian categories, Grothendieck categories (18E10) Other classes of modules and ideals in associative algebras (16D80) Abstract manifolds and fiber bundles (category-theoretic aspects) (18F15)

Related Items (5)

Derived dualities induced by a 1-cotilting bimodule ⋮ Purity in compactly generated derivators and t-structures with Grothendieck hearts ⋮ Cotilting sheaves over weighted noncommutative regular projective curves ⋮ Tilting and cotilting modules over concealed canonical algebras ⋮ Derived equivalences induced by big cotilting modules

Cites Work

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• Tilting objects in abelian categories and quasitilted rings
• Cotilting modules are pure-injective
• Tilting in Grothendieck categories
• Tilting in abelian categories and quasitilted algebras
• Infinite Dimensional Representations of Canonical Algebras
• Tilting preenvelopes and cotilting precovers

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