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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