Foxby equivalence over associative rings
Abstract
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 paper contains a few results which are new in the commutative, noetherian setting.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- November 2006
- DOI:
- 10.48550/arXiv.math/0611838
- arXiv:
- arXiv:math/0611838
- Bibcode:
- 2006math.....11838H
- Keywords:
-
- Mathematics - Commutative Algebra;
- Mathematics - Rings and Algebras;
- 13D02;
- 13D07;
- 13D25;
- 16E05;
- 16E30
- E-Print:
- 24 pages