Covers and envelopes related to divisibility

DOI10.1007/S40590-023-00544-WOpenAlexW4387084669MaRDI QIDQ6080935

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Publication date: 25 October 2023

Published in: Boletín de la Sociedad Matemática Mexicana. Third Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40590-023-00544-w

zbMATH Keywords

(pre)cover(pre)envelopetight systemtight submoduleweak-injective module(almost) perfect ring\((h)\)-divisible modulesubperfect ring

Mathematics Subject Classification ID

Other special types of modules and ideals in commutative rings (13C13) Injective and flat modules and ideals in commutative rings (13C11)

Cites Work

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• Relative homological algebra. Vol. 2
• Generalized Hill lemma, Kaplansky theorem for cotorsion pairs and some applications.
• Injective and flat covers, envelopes and resolvents
• Almost perfect commutative rings
• From a single chain to a large family of submodules
• One dimensional tilting modules are of finite type.
• Approximations and endomorphism algebras of modules.
• Cotorsion pairs generated by modules of bounded projective dimension.
• ALL MODULES HAVE FLAT COVERS
• Finitistic Dimension and a Homological Generalization of Semi-Primary Rings
• Divisible Modules
• Direct Products of Modules
• Cotorsion and Tor Pairs and Finitistic Dimensions over Commutative Rings
• Absolutely Pure Covers
• The Functor Hom and Cotorsion Theories
• Rings characterized by (pre)envelopes and (pre)covers of their modules^∗
• Almost perfect domains
• DIVISIBLE ENVELOPES, $\mathcal{P}_1$-COVERS AND WEAK-INJECTIVE MODULES
• Weak and injective dimensional analogues of Kaplansky’s and Auslander’s lemmas for purity
• CHARACTERIZING ALMOST PERFECT RINGS BY COVERS AND ENVELOPES
• Weak-Injective Modules
• Tilting Cotorsion Pairs

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