Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A NOTE ON GORENSTEIN PRÜFER 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 Mathematics and Software Science Sichuan Normal University)
  • Received : 2015.09.17
  • Published : 2016.09.30
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Abstract

In this note, we mainly discuss the Gorenstein $Pr{\ddot{u}}fer$ domains. It is shown that a domain is a Gorenstein $Pr{\ddot{u}}fer$ domain if and only if every finitely generated ideal is Gorenstein projective. It is also shown that a domain is a PID (resp., Dedekind domain, $B{\acute{e}}zout$ domain) if and only if it is a Gorenstein $Pr{\ddot{u}}fer$ UFD (resp., Krull domain, GCD domain).

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