On preenvelopes and precovers by ideals of morphisms of modules

DOI10.1016/j.jpaa.2018.02.017zbMath1427.16003OpenAlexW2790665331MaRDI QIDQ1651495

Li-Xin Mao

Publication date: 12 July 2018

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

Full work available at URL: https://doi.org/10.1016/j.jpaa.2018.02.017

zbMATH Keywords

closure properties\(\mathcal{I}\)-precovers\(\mathcal{I}\)-preenvelopes

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Relative homological algebra, projective classes (category-theoretic aspects) (18G25)

Cites Work

• Contravariant functors on the category of finitely presented modules.
• Injective and flat covers, envelopes and resolvents
• Preprojective modules over Artin algebras
• On ideals and homology in additive categories
• Flat covers of modules
• Relative homological algebra
• The phantom cover of a module.
• Ideal approximation theory
• Covering ideals of morphisms and module representations of the quiver \(\mathbb A_2\).
• Approximations and endomorphism algebras of modules.
• Flat covers and cotorsion envelopes of sheaves
• Powers of the phantom ideal
• Covers in finitely accessible categories
• Locally finitely presented additive categories
• Higher phantom and Ext-phantom morphisms