On *w-Finiteness Conditions

Jung Wook Lim

doi:10.5666/KMJ.2023.63.4.571

On *_w-Finiteness Conditions

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Abstract

Let D be an integral domain and let * be a star-operation on D. In this article, we give new characterizations of *_w-Noetherian domains and *_w-principal ideal domains. More precisely, we show that D is a *_w-Noetherian domain (resp., *_w-principal ideal domain) if and only if every *_w-countable type ideal of D is of *_w-finite type (resp., principal).

Original language	English
Pages (from-to)	571-575
Number of pages	5
Journal	Kyungpook Mathematical Journal
Volume	63
Issue number	4
DOIs	https://doi.org/10.5666/KMJ.2023.63.4.571
State	Published - 2023

Keywords

,-countable type ideal
,-Noetherian domain
,-principal ideal domain

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On *_w-Finiteness Conditions

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Keywords

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