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Classifying subcategories of modules


Author: Mark Hovey
Journal: Trans. Amer. Math. Soc. 353 (2001), 3181-3191
MSC (2000): Primary 13C05, 18E30, 18G35
DOI: https://doi.org/10.1090/S0002-9947-01-02747-7
Published electronically: April 12, 2001
Erratum: Tran. Amer. Math. Soc. 360 (2008), 2809-2809
MathSciNet review: 1828603
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Abstract:

Let $R$ be the quotient of a regular coherent commutative ring by a finitely generated ideal. In this paper, we classify all abelian subcategories of finitely presented $R$-modules that are closed under extensions. We also classify abelian subcategories of arbitrary $R$-modules that are closed under extensions and coproducts, when $R$ is commutative and Noetherian. The method relies on comparison with the derived category of $R$.

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Additional Information

Mark Hovey
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
Email: hovey@member.ams.org

DOI: https://doi.org/10.1090/S0002-9947-01-02747-7
Received by editor(s): January 15, 2000
Received by editor(s) in revised form: June 19, 2000
Published electronically: April 12, 2001
Article copyright: © Copyright 2001 American Mathematical Society