J. Korean Math. Soc. 2023; 60(3): 683-694
Online first article April 21, 2023 Printed May 1, 2023
https://doi.org/10.4134/JKMS.j220479
Copyright © The Korean Mathematical Society.
Zhongkui Liu, Pengju Ma, Xiaoyan Yang
Northwest Normal University; Northwest Normal University; Northwest Normal University
Let $\mathfrak{a}$ be an ideal of a commutative noetherian ring $R$. We give some descriptions of the $\mathfrak{a}$-depth of $\mathfrak{a}$-relative Cohen-Macaulay modules by cohomological dimensions, and study how relative Cohen-Macaul-\\ayness behaves under flat extensions. As applications, the perseverance of relative Cohen-Macaulayness in a polynomial ring, formal power series ring and completion are given.
Keywords: Relative Cohen-Macaulay module, $\mathfrak{a}$-depth, cohomological dimension
MSC numbers: Primary 13C15, 13H10
Supported by: The authors thank the referee for important comments and suggestions on improving this paper. This research was partially supported by National Natural Science Foundation of China (11901463), graduate Research Fund project of Northwest Normal University (2021KYZZ01031) and Gansu Province outstanding graduate student ``Innovation Star'' project (2022CXZX-238).
2015; 52(6): 1253-1270
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