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Resolutions and Stability of Gorenstein Classes of Modules

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Abstract

Let \(\mathcal {X}\), \(\mathcal {U}\) and \(\mathcal {Z}\) be classes of left R-modules, \(\mathcal {W}\) be a class of right R-modules and \(\mathcal {X}\subseteq \mathcal {U}\). In this paper, we investigate the relationship between \(\mathcal {Z}\)-proper (resp. \(\mathcal {Z}\)-coproper, \(\mathcal {W}\)-pure) \(\mathcal {U}\)-(co)resolutions and \(\mathcal {Z}\)-proper (resp. \(\mathcal {Z}\)-coproper, \(\mathcal {W}\)-pure) \(\mathcal {X}\)-(co)resolutions. As applications, we give an affirmative answer to the stability question on Gorenstein classes of modules, which unify the corresponding results possessed by some known Gorenstein classes of modules.

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Acknowledgements

The author would like to express her sincere thanks to the referees for their helpful suggestions and comments, which have greatly improved the paper.

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  1. Department of Mathematics, Northwest Normal University, Lanzhou, China

    Zhanping Wang

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  1. Zhanping Wang
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Correspondence to Zhanping Wang.

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Communicated by Shiping Liu.

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Supported by National Natural Science Foundation of China (Grant No. 11561061).

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Wang, Z. Resolutions and Stability of Gorenstein Classes of Modules. Bull. Malays. Math. Sci. Soc. 43, 1493–1502 (2020). https://doi.org/10.1007/s40840-019-00752-6

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  • DOI: https://doi.org/10.1007/s40840-019-00752-6

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