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Gorenstein Homological Properties and Quasi-Frobenius Bimodules

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Abstract

We establish relations of Gorenstein homological properties of modules and rings linked by a fixed quasi-Frobenius bimodule. Particularly, let \(R\subset S\) be a strongly separable quasi-Frobenius extension. The left Gorenstein global dimensions and the left finitistic Gorenstein projective dimensions of rings S and R are equal. Moreover, R is left-Gorenstein (Cohen–Macaulay finite, Cohen–Macaulay free) if and only if so is S.

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Acknowledgements

The authors wish to express their gratitude to the referee for his careful reading and comments which improve the presentation of this article.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Hanjiang Normal University, Shiyan, 442000, China

    Chaoling Huang

  2. Hubei Key Laboratory of Applied Mathematics (Hubei University), Wuhan, 430062, China

    Chaoling Huang

  3. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Yongliang Sun

  4. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Yanbo Zhou

Authors
  1. Chaoling Huang
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  2. Yongliang Sun
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  3. Yanbo Zhou
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Correspondence to Chaoling Huang.

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Communicated by Santiago Zarzuela.

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The first author is supported by Open Foundation of Hubei Key Laboratory of Applied Mathematics (Hubei University No. HBAM202002), the Project of Humanity and Social Science Research of Hubei Province China (No. 18Q189) and the Plan of Science and Technology Innovation Team of Excellent Young and Middle-age of Hubei Province (No. T201731); the third author is supported by the National Nature Science Foundation of China (No. 11801464).

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Huang, C., Sun, Y. & Zhou, Y. Gorenstein Homological Properties and Quasi-Frobenius Bimodules. Bull. Iran. Math. Soc. 48, 805–817 (2022). https://doi.org/10.1007/s41980-021-00548-0

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  • DOI: https://doi.org/10.1007/s41980-021-00548-0

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