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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on $ *_w$-Noetherian domains


Authors: Chul Ju Hwang and Jung Wook Lim
Journal: Proc. Amer. Math. Soc. 141 (2013), 1199-1209
MSC (2010): Primary 13A15, 13G05; Secondary 13E99, 13F05, 13F20
Published electronically: August 30, 2012
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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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Additional Information

Chul Ju Hwang
Affiliation: Department of Mathematics Education, Silla University, Pusan 617-736, Republic of Korea
Email: cjhwang@silla.ac.kr

Jung Wook Lim
Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea
Email: lovemath@postech.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-10706-3
PII: S 0002-9939(2012)10706-3
Keywords: $*_{w}$-operation, $*_{w}$-Noetherian domain.
Received by editor(s): June 3, 2010
Received by editor(s) in revised form: August 18, 2011
Published electronically: August 30, 2012
Additional Notes: The authors thank the referee for valuable suggestions
Communicated by: Irena Peeva
Article copyright: © Copyright 2012 American Mathematical Society