Classifying Serre subcategories via atom spectrum

Abstract

In this paper, we introduce the atom spectrum of an abelian category as a topological space consisting of all the equivalence classes of monoform objects. In terms of the atom spectrum, we give a classification of Serre subcategories of an arbitrary noetherian abelian category. Moreover we show that the atom spectrum of a locally noetherian Grothendieck category is homeomorphic to its Ziegler spectrum.

15 pages

References in corpus (2)

• Classifying subcategories of modules over a commutative noetherian ring
• A one-sided Prime Ideal Principle for noncommutative rings

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