Auslander-type conditions and cotorsion pairs
نویسندگان
چکیده
منابع مشابه
Auslander-type conditions and cotorsion theory
We study the properties of rings satisfying Auslander-type conditions. If an artin algebra Λ satisfies the Auslander condition (that is, Λ is an ∞-Gorenstein artin algebra), then we construct two kinds of subcategories which form functorially finite cotorsion theories. Noetherian rings satisfying ‘Auslander-type conditions’ on self-injective resolutions can be regarded as certain non-commutativ...
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We prove that the Auslander class determined by a semidualizing module is the left half of a perfect cotorsion pair. We also prove that the Bass class determined by a semidualizing module is preenveloping. 0. Introduction The notion of semidualizing modules over commutative noetherian rings goes back to Foxby [11] and Golod [13]. Christensen [3] extended this notion to semidualizing complexes. ...
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Throughout this article, Λ is a left and right Noetherian ring (unless stated otherwise), modΛ is the category of finitely generated left Λ-modules and 0 → Λ → I0(Λ) → I1(Λ) → · · · → Ii(Λ) → · · · is the minimal injective resolution of Λ as a left Λ-module. For a module M ∈ mod Λ and a non-negative integer n, recall that the grade of M , denoted by gradeM , is said to be at least n if ExtΛ(M, ...
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Let R be a ring and T be a 1-tilting right R-module. Then T is of countable type. Moreover, T is of finite type in case R is a Prüfer domain.
متن کاملCotorsion pairs and model categories
The purpose of this paper is to describe a connection between model categories, a structure invented by algebraic topologists that allows one to introduce the ideas of homotopy theory to situations far removed from topological spaces, and cotorsion pairs, an algebraic notion that simultaneously generalizes the notion of projective and injective objects. In brief, a model category structure on a...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.09.010