대한수학회지 (Journal of the Korean Mathematical Society)

  • 제60권3호
  • /
  • Pages.683-694
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  • 2023
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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ON RELATIVE COHEN-MACAULAY MODULES

  • Zhongkui Liu (Department of Mathematics Northwest Normal University) ;
  • Pengju Ma (Department of Mathematics Northwest Normal University) ;
  • Xiaoyan Yang (Department of Mathematics Northwest Normal University)
  • 투고 : 2022.09.21
  • 심사 : 2023.02.14
  • 발행 : 2023.05.01
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초록

Let a be an ideal of 𝔞 commutative noetherian ring R. We give some descriptions of the 𝔞-depth of 𝔞-relative Cohen-Macaulay modules by cohomological dimensions, and study how relative Cohen-Macaulayness behaves under flat extensions. As applications, the perseverance of relative Cohen-Macaulayness in a polynomial ring, formal power series ring and completion are given.

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과제정보

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).

참고문헌

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