Subcategories of extension modules by Serre subcategories

Yoshizawa, Takeshi

doi:10.1090/S0002-9939-2011-11108-0

Subcategories of extension modules by Serre subcategories
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by Takeshi Yoshizawa

Proc. Amer. Math. Soc. 140 (2012), 2293-2305

DOI: https://doi.org/10.1090/S0002-9939-2011-11108-0

Published electronically: November 23, 2011

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Abstract:

In 1962, P. Gabriel showed the existence of a lattice isomorphism between the set of Serre subcategories of the category consisting of finitely generated modules and the set of specialization closed subsets of the set of prime ideals. In this paper, we consider subcategories consisting of the extensions of modules in two given Serre subcategories to find a method of constructing Serre subcategories of the category of modules. We shall give a criterion for this subcategory to be a Serre subcategory.

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