Generalized Hill lemma, Kaplansky theorem for cotorsion pairs and some applications.

DOI10.1216/RMJ-2009-39-1-305zbMath1173.16004WikidataQ57571188 ScholiaQ57571188MaRDI QIDQ1011145

Jan Šťovíček, Jan Trlifaj

Publication date: 7 April 2009

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

filtrationscotorsion pairsMatlis localizationsHill lemmastrongly flat modules

Mathematics Subject Classification ID

Free, projective, and flat modules and ideals in associative algebras (16D40) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Integral domains (13G05) Valuation rings (13F30) Torsion-free groups, infinite rank (20K20) Injective and flat modules and ideals in commutative rings (13C11) Rings of fractions and localization for commutative rings (13B30) Filtered associative rings; filtrational and graded techniques (16W70)

Related Items (12)

A model structure approach to the finitistic dimension conjectures ⋮ Covers, envelopes, and cotorsion theories in locally presentable abelian categories and contramodule categories ⋮ Cotorsion pairs generated by modules of bounded projective dimension. ⋮ Categoricity for transfinite extensions of modules ⋮ Covers and envelopes related to divisibility ⋮ Almost free modules and Mittag-Leffler conditions. ⋮ Shortening filtrations. ⋮ A new version of a theorem of Kaplansky ⋮ Model category structures arising from Drinfeld vector bundles ⋮ Telescope conjecture, idempotent ideals, and the transfinite radical ⋮ The countable telescope conjecture for module categories. ⋮ Deconstructibility and the Hill Lemma in Grothendieck categories

Cites Work

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• The Third Axiom of Countability for Abelian Groups
• S-divisible modules over domains
• Completeness of cotorsion pairs
• Tilting Cotorsion Pairs

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