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GORENSTEIN MODULES AND GORENSTEIN MODEL STRUCTURES

Part of: Homological algebra

Published online by Cambridge University Press:  27 February 2017

AIMIN XU
AIMIN XU*
Affiliation:
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China e-mail: [email protected]
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Abstract

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Given a complete hereditary cotorsion pair $(\mathcal{X}, \mathcal{Y})$, we introduce the concept of $(\mathcal{X}, \mathcal{X} \cap \mathcal{Y})$-Gorenstein projective modules and study its stability properties. As applications, we first get two model structures related to Gorenstein flat modules over a right coherent ring. Secondly, for any non-negative integer n, we construct a cofibrantly generated model structure on Mod(R) in which the class of fibrant objects are the modules of Gorenstein injective dimension ≤ n over a left Noetherian ring R. Similarly, if R is a left coherent ring in which all flat left R-modules have finite projective dimension, then there is a cofibrantly generated model structure on Mod(R) such that the cofibrant objects are the modules of Gorenstein projective dimension ≤ n. These structures have their analogous in the category of chain complexes.

MSC classification

Primary: 18G25: Relative homological algebra, projective classes
Secondary: 18G10: Resolutions; derived functors
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 3 , September 2017 , pp. 685 - 703
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

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