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

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 * w a star-operation on D defined by I * w = {x ∈ K | Jx ⊆ I for some J ∈ GV * (D)} for all nonzero fractional ideals I of D. In this article, we give a simple proof of Hilbert basis theorem for * w -Noetherian domains.