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Let be a locally coherent Grothendieck category, be the full subcategory of consisting of finitely presented objects and be the atom spectrum of . In this paper, we classify localizing subcategories of finite type of via open subsets of . We investigate and show that if , then is locally noetherian. As an application, we specialize our investigation to the case of commutative coherent rings.

生成讲解博客的中文版本

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