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A GORENSTEIN HOMOLOGICAL CHARACTERIZATION OF KRULL DOMAINS

  • Shiqi Xing (College of Applied Mathematics Chengdu University of Information Technology) ;
  • Xiaolei Zhang (School of Mathematics and Statistics Shandong University of Technology)
  • Received : 2023.05.26
  • Accepted : 2023.07.21
  • Published : 2024.05.31
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Abstract

In this note, we shed new light on Krull domains from the point view of Gorenstein homological algebra. By using the so-called w-operation, we show that an integral domain R is Krull if and only if for any nonzero proper w-ideal I, the Gorenstein global dimension of the w-factor ring (R/I)w is zero. Further, we obtain that an integral domain R is Dedekind if and only if for any nonzero proper ideal I, the Gorenstein global dimension of the factor ring R/I is zero.

Keywords

Acknowledgement

The author would like to thank the referee for comments and corrections. The first named author is supported by the Scientific Research Foundation of Chengdu University of Information Technology (KYTZ202015, 2022ZX001).

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