J. Korean Math. Soc. 2024; 61(3): 603-620
Online first article April 11, 2024 Printed May 1, 2024
https://doi.org/10.4134/JKMS.j230462
Copyright © The Korean Mathematical Society.
yanjie Li, Renyu Zhao
Northwest Normal University; and Statistics
Let $\mathcal{V}$, $\mathcal{W}$, $\mathcal{Y}$, $\mathcal{X}$ be four classes of left $R$-modules. The notion of $(\mathcal{V, W, Y, X})$-Gorenstein $R$-complexes is introduced, and it is shown that under certain mild technical assumptions on $\mathcal{V}$, $\mathcal{W}$, $\mathcal{Y}$, $\mathcal{X}$, an $R$-complex ${M}$ is $(\mathcal{V, W, Y, X})$-Gorenstein if and only if the module in each degree of ${M}$ is $(\mathcal{V, W, Y, X})$-Gorenstein and the total Hom complexs Hom$_R({Y},{M})$, Hom$_R({M},{X})$ are exact for any ${Y}\in\widetilde{\mathcal{Y}}$ and any ${X}\in\widetilde{\mathcal{X}}$. Many known results are recovered, and some new cases are also naturally generated.
Keywords: Gorenstein module, Gorenstein complex
MSC numbers: Primary 18G25, 18G35
Supported by: This work was financially supported by the National Natural Science Foundation of China (Grant nos. 11861055, 12061061 and 12361008) and Funds for Innovative Fundamental Research Group Project of Gansu Province (Grant no. 23JRRA684).
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