Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON OVERRINGS OF GORENSTEIN DEDEKIND DOMAINS

  • Hu, Kui (College of Science Southwest University of Science and Technology) ;
  • Wang, Fanggui (College of Mathematics and Software Science Sichuan Normal University) ;
  • Xu, Longyu (College of Science Southwest University of Science and Technology) ;
  • Zhao, Songquan (College of Science Southwest University of Science and Technology)
  • Received : 2012.09.27
  • Published : 2013.09.01
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Abstract

In this paper, we mainly discuss Gorenstein Dedekind do-mains (G-Dedekind domains for short) and their overrings. Let R be a one-dimensional Noetherian domain with quotient field K and integral closure T. Then it is proved that R is a G-Dedekind domain if and only if for any prime ideal P of R which contains ($R\;:_K\;T$), P is Gorenstein projective. We also give not only an example to show that G-Dedekind domains are not necessarily Noetherian Warfield domains, but also a definition for a special kind of domain: a 2-DVR. As an application, we prove that a Noetherian domain R is a Warfield domain if and only if for any maximal ideal M of R, $R_M$ is a 2-DVR.

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