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Cotorsion pairs and model structures on Ch(R)

Part of: Commutative algebra: Homological methods Homological algebra

Published online by Cambridge University Press:  17 August 2011

Gang Yang  and
Zhongkui Liu
Gang Yang
Affiliation:
School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, People's Republic of China (yanggang10@gmail.com) College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, People's Republic of China (liuzk@nwnu.edu.cn)
Zhongkui Liu
Affiliation:
College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, People's Republic of China (liuzk@nwnu.edu.cn)
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Abstract

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We show that if the given cotorsion pair in the category of modules is complete and hereditary, then both of the induced cotorsion pairs in the category of complexes are complete. We also give a cofibrantly generated model structure that can be regarded as a generalization of the projective model structure.

Keywords

(pre)envelopes(pre)coverscotorsion pairsprojective dimension of complexesmodel structures

MSC classification

Secondary: 13D05: Homological dimension 13D07: Homological functors on modules (Tor, Ext, etc.) 18G15: Ext and Tor, generalizations, Künneth formula 18G35: Chain complexes 18G55: Homotopical algebra
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 3 , October 2011 , pp. 783 - 797
Copyright
Copyright © Edinburgh Mathematical Society 2011

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