Integrality of noetherian Grothendieck categories
نویسندگان
چکیده
We introduce the notion of integrality Grothendieck categories as a simultaneous generalization primeness noncommutative noetherian rings and locally schemes. Two different spaces associated to category yield respective definitions integrality, we prove equivalence these using Grothendieck-categorical version Gabriel's correspondence, which originally related indecomposable injective modules prime two-sided ideals for rings. The is also used classify closed localizing subcategories. As an application main results, develop theory singular objects in deduce Goldie's theorem on existence quotient ring its consequence.
منابع مشابه
Non-noetherian Grothendieck Duality
For any separated map f : X → Y of quasi-compact quasiseparated schemes, Rf∗ : D + qc(X) → D (Y ) has a right adjoint f . If f is proper and pseudo-coherent (e.g., finitely-presented and flat) then Duality and tor-independent Base Change hold for f . Preface This is a research summary written early in 1991, concerning results obtained by the author during a stay at MSRI in Berkeley during 1989–...
متن کاملAtomical Grothendieck Categories
Motivated by the study of Gabriel dimension of a Grothendieck category, we introduce the concept of atomical Grothendieck category, which has only two localizing subcategories, and we give a classification of this type of Grothendieck categories. 1. Introduction. Given a Grothendieck category Ꮽ, we can associate with it the lattice of all localizing categories of Ꮽ and denote it by Tors(Ꮽ). We ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2022
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2021.10.036