From submodule categories to the stable Auslander algebra
نویسندگان
چکیده
منابع مشابه
Symmetric Auslander and Bass Categories
We define the symmetric Auslander category A(R) to consist of complexes of projective modules whose leftand righttails are equal to the leftand right-tails of totally acyclic complexes of projective modules. The symmetric Auslander category contains A(R), the ordinary Auslander category. It is well known that A(R) is intimately related to Gorenstein projective modules, and our main result is th...
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Let R be a homomorphic image of a Gorenstein local ring. Recent work has shown that there is a bridge between Auslander categories and modules of finite Gorenstein homological dimensions over R. We use Gorenstein dimensions to prove new results about Auslander categories and vice versa. For example, we establish base change relations between the Auslander categories of the source and target rin...
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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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We introduce and develop an analogous of the AuslanderBuchweitz approximation theory (see [2]) in the context of triangulated categories, by using a version of relative homology in this setting. We also prove several results concerning relative homological algebra in a triangulated category T , which are based on the behavior of certain subcategories under finiteness of resolutions and vanishin...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2017
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2017.05.012