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 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...