Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOME ONE-DIMENSIONAL NOETHERIAN DOMAINS AND G-PROJECTIVE MODULES

  • Kui Hu (College of Science Southwest University of Science and Technology) ;
  • Hwankoo Kim (Division of Computer Engineering Hoseo University) ;
  • Dechuan Zhou (College of Science Southwest University of Science and Technology)
  • Received : 2022.07.24
  • Accepted : 2023.10.05
  • Published : 2023.11.30
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Abstract

Let R be a one-dimensional Noetherian domain with quotient field K and T be the integral closure of R in K. In this note we prove that if the conductor ideal (R :K T) is a nonzero prime ideal, then every finitely generated reflexive (and hence finitely generated G-projective) R-module is isomorphic to a direct sum of some ideals.

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Acknowledgement

The authors would like to thank the reviewer for his/her careful reading and comments.

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