• Title/Summary/Keyword: n-strongly Gorenstein projective module

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ON OVERRINGS OF GORENSTEIN DEDEKIND DOMAINS

  • Hu, Kui;Wang, Fanggui;Xu, Longyu;Zhao, Songquan
    • Journal of the Korean Mathematical Society
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    • v.50 no.5
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    • pp.991-1008
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    • 2013
  • 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.