Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A SIMPLE PROOF OF HILBERT BASIS THEOREM FOR *ω-NOETHERIAN DOMAINS

  • Lim, Jung Wook (Department of Mathematics Kyungpook National University) ;
  • Oh, Dong Yeol (Division of Liberal Arts Hanbat National University)
  • Received : 2013.04.07
  • Accepted : 2013.06.01
  • Published : 2013.06.30
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Abstract

Let D be an integral domain with quotient field K, * a star-operation on D, $GV^*(D)$ the set of nonzero finitely generated ideals J of D such that $J_*=D$, and $*_{\omega}$ a star-operation on D defined by $I_{*_{\omega}}=\{x{\in}K{\mid}Jx{\subseteq}I\;for\;some\;J{\in}GV^*(D)\}$ for all nonzero fractional ideals I of D. In this article, we give a simple proof of Hilbert basis theorem for $*_{\omega}$-Noetherian domains.

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References

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