A note on *_{𝑤}-Noetherian domains

Hwang, Chul Ju; Lim, Jung Wook

doi:10.1090/S0002-9939-2012-10706-3

A note on $*_w$-Noetherian domains
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by Chul Ju Hwang and Jung Wook Lim PDF

Proc. Amer. Math. Soc. 141 (2013), 1199-1209 Request permission

Abstract:

Let $D$ be an integral domain with quotient field $K$, $*$ be a star-operation on $D$, and $GV^*(D)$ be the set of finitely generated ideals $J$ of $D$ such that $J_*=D$. Then the map $*_w$ defined by $I_{*_w}=\{x \in K \mid Jx \subseteq I$ for some $J \in GV^*(D)\}$ for all nonzero fractional ideals $I$ of $D$ is a finite character star-operation on $D$. In this paper, we study several properties of $*_w$-Noetherian domains. In particular, we prove the Hilbert basis theorem for $*_w$-Noetherian domains.

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