Korean J. Math.  Vol 21, No 2 (2013)  pp.197-201
DOI: https://doi.org/10.11568/kjm.2013.21.2.197

A simple proof of Hilbert basis theorem for $*_w$-Noetherian domains

Jung Wook Lim, Dong Yeol Oh

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 $I_{*_w}=\{x \in K \mid Jx \subseteq I$ for some $J \in {\rm GV}^*(D)\}$ for all nonzero fractional ideals $I$ of $D$. In this article, we give a simple proof of Hilbert basis theorem for $*_w$-Noetherian domains.

Subject classification

13E99, 13A15, 13B25, 13G05

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ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr