Remarks on subcategories of artinian modules

Mathematics – Commutative Algebra

Scientific paper

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14 pages

Scientific paper

We study two subcategories of the category of artinian modules, a wide
subcategory and a Serre subcategory. We prove that all wide subcategories of
artinian modules are Serre subcategories. We also provide the bijection between
the set of Serre subcategories and the set of specialization closed subsets of
the set of closed prime ideals of some completed ring.

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