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Some remarks on projective generators and injective cogenerators

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Abstract

In this paper, we give a relationship between projective generators (resp., injective cogenerators) in the category of R-modules and the counterparts in the category of complexes of R-modules. As a consequence, we get that complexes of W-Gorenstein modules are actually -Gorenstein complexes whenever W is a subcategory of R-modules satisfying W ⊥ W, where is the subcategory of exact complexes with all cycles in W. We also study when all cycles of a -Gorenstein complexes are W-Gorenstein modules.

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Authors and Affiliations

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, 730070, P. R. China

    Li Liang & Gang Yang

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, P. R. China

    Nan Qing Ding

Authors
  1. Li Liang
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  2. Nan Qing Ding
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  3. Gang Yang
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Correspondence to Li Liang.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11301240, 11371187 and 11101197), and the Young Scholars Science Foundation of Lanzhou Jiaotong University (Grant No. 2012020)

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Liang, L., Ding, N.Q. & Yang, G. Some remarks on projective generators and injective cogenerators. Acta. Math. Sin.-English Ser. 30, 2063–2078 (2014). https://doi.org/10.1007/s10114-014-3227-z

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  • DOI: https://doi.org/10.1007/s10114-014-3227-z

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