Moroccan Journal of Algebra and Geometry with Applications
Cotorsion theory and its application to ring structures – a book chapter
Fanggui Wang and Hwankoo Kim
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, PR China
Division of Computer Engineering, Hoseo University, Asan 31499, Republic of Korea
Pages 286-360 | Received 02 April 2022, Accepted 24 July 2022, Published 06 December 2022
Abstract
In this survey article, we introduce the properties of the cotorsion theory and show how to construct the homology theory for all cotorsion theories. This can be considered the final chapter of the author’s book entitled “Foundations of Commutative Rings and Their Modules” published by Springer in 2016.
Keywords: cotorsion theory, hereditary cotorsion theory, complete cotorsion theory, perfect cotorsion theory, pure submodule, Tor-orthocomplement, (pre)cover, (pre)envelope, resolving class, coresolving class, weak w-projective module, Kaplansky’s theorem, w-split module, n-cotorsion module, n-torsion-free module, n-Warfield cotorsion module, weak finitistic dimension, Matlis cotorsion module, Matlis domain, Almost perfect domain, n-perfect ring, strongly flat module, Prüfer domain, G-Dedekind domain.
MSC numbers: Primary 13C10, 13DXX; Secondary 13C11, 13C12, 13C13, 13F05, 13F30, 13G05, 13H99.
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