Subcategories of extension modules by Serre subcategories
Takeshi Yoshizawa
TL;DR
This paper investigates how to construct Serre subcategories of modules by examining extensions of modules within given Serre subcategories, providing criteria for when these extensions form Serre subcategories.
Contribution
It introduces a method and criterion for forming Serre subcategories through extensions of modules in existing Serre subcategories.
Findings
Provides a criterion for extension subcategories to be Serre subcategories
Develops a method to construct Serre subcategories from existing ones
Enhances understanding of the structure of module categories
Abstract
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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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras · Algebraic Geometry and Number Theory