A SIMPLE PROOF OF HILBERT BASIS THEOREM FOR *ω-NOETHERIAN DOMAINS

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.