§15.54, “Abelian categories of modules¶
The Stacks Project. §15.54, “Abelian categories of modules.
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Domain-specific¶
- Category of Modules
- For a non-Noetherian commutative ring, finitely generated modules can fail to form an abelian subcategory: if \(I\) is a non-finitely-generated ideal, the map \(R\to R/I\) has no kernel object within that restricted category.
This sourceThe finitely generated counterexample and Noetherian repair here are confined to that scope.
- For a non-Noetherian commutative ring, finitely generated modules can fail to form an abelian subcategory: if \(I\) is a non-finitely-generated ideal, the map \(R\to R/I\) has no kernel object within that restricted category.
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