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Homological Properties of Modules with Finite Weak Injective and Weak Flat Dimensions

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Abstract

In this paper, we define a class of relative derived functors in terms of left or right weak flat resolutions to compute the weak flat dimension of modules. Moreover, we investigate two classes of modules larger than those of weak injective and weak flat modules, study the existence of covers and preenvelopes, and give some applications.

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Acknowledgments

The author would like to thank the referees for their careful reading and valuable remarks that improved the presentation of this work. He also thanks Professor Zhaoyong Huang for his encouragement. This research was partially supported by NSFC (Grant No. 11571164) and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, Jiangsu Province, People’s Republic of China

    Tiwei Zhao

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  1. Tiwei Zhao
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Correspondence to Tiwei Zhao.

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Communicated by Shiping Liu.

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Zhao, T. Homological Properties of Modules with Finite Weak Injective and Weak Flat Dimensions. Bull. Malays. Math. Sci. Soc. 41, 779–805 (2018). https://doi.org/10.1007/s40840-016-0365-8

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  • DOI: https://doi.org/10.1007/s40840-016-0365-8

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