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. ...

Let R be a commutative noetherian local ring with completion b R. When R has the approximation property, we prove an approximation result for complexes with finitely generated homology. This is used to investigate descent of semidualizing complexes from b R to R. We show that, if R has the approximation property, then there is a bijective correspondence between semidualizing b R-complexes and s...

We extend the definition of a semidualizing module to associative rings. This enables us to define and study Auslander and Bass classes with respect to a semidualizing bimodule C. We then study the classes of C-flats, C-projectives, and C-injectives, and use them to provide a characterization of the modules in the Auslander and Bass classes. We extend Foxby equivalence to this new setting. This...

We study the following question: Given two semidualizing complexes B and C over a commutative noetherian ring R, does the vanishing of Ext R (B, C) for n ≫ 0 imply that B is C-reflexive? This question is a natural generalization of one studied by Avramov, Buchweitz, and Şega. We begin by providing conditions equivalent to B being C-reflexive, each of which is slightly stronger than the conditio...

We study the following question: Given two semidualizing complexes B and C over a commutative noetherian ring R, does the vanishing of Ext R (B, C) for n ≫ 0 imply that B is C-reflexive? This question is a natural generalization of one studied by Avramov, Buchweitz, and Şega. We begin by providing conditions equivalent to B being C-reflexive, each of which is slightly stronger than the conditio...

Let R be a commutative noetherian ring. The n-semidualizing modules of are generalizations its semidualizing modules. We will prove some basic properties Our main result and example shows that the divisor class group Gorenstein determinantal ring over field is set isomorphism classes 1-semidualizing Finally, we pose questions about

We prove versions of results of Foxby and Holm about modules of finite (Gorenstein) injective dimension and finite (Gorenstein) projective dimension with respect to a semidualizing module. We also verify two special cases of a question of Takahashi and White.

We introduce and study a class of objects that encompasses Christensen Foxby’s semidualizing modules complexes Kubik’s quasi-dualizing modules: the [Formula: see text]-adic complexes. give examples equivalent characterizations these objects, including characterization in terms more familiar property. As an application, we proof existence dualizing over complete local rings does not use Cohen St...