On *ω-Finiteness Conditions

초록

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

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