Journal of Mathematics of Kyoto University

Foxby equivalence over associative rings

Abstract

We extend the definition of a semidualizing module to general 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 even in the commutative, noetherian setting.

Article information

Source
J. Math. Kyoto Univ., Volume 47, Number 4 (2007), 781-808.

Dates
First available in Project Euclid: 19 August 2009

https://projecteuclid.org/euclid.kjm/1250692289

Digital Object Identifier
doi:10.1215/kjm/1250692289

Mathematical Reviews number (MathSciNet)
MR2413065

Zentralblatt MATH identifier
1154.16007

Citation

Holm, Henrik; White, Diana. Foxby equivalence over associative rings. J. Math. Kyoto Univ. 47 (2007), no. 4, 781--808. doi:10.1215/kjm/1250692289. https://projecteuclid.org/euclid.kjm/1250692289