## Kodai Mathematical Journal

### Foxby equivalences associated to strongly Gorenstein modules

#### Abstract

In order to establish the Foxby equivalences associated to strongly Gorenstein modules, we introduce the notions of strongly $\mathcal{W}_P$-Gorenstein, $\mathcal{W}_I$-Gorenstein and $\mathcal{W}_F$-Gorenstein modules and discuss some basic properties of these modules. We show that the subcategory of strongly Gorenstein projective left $R$-modules in the left Auslander class and the subcategory of strongly $\mathcal{W}_P$-Gorenstein left $S$-modules are equivalent under Foxby equivalence. The injective and flat case are also studied.

#### Article information

Source
Kodai Math. J., Volume 41, Number 2 (2018), 397-412.

Dates
First available in Project Euclid: 2 July 2018

https://projecteuclid.org/euclid.kmj/1530496849

Digital Object Identifier
doi:10.2996/kmj/1530496849

Mathematical Reviews number (MathSciNet)
MR3824858

Zentralblatt MATH identifier
06936460

#### Citation

Zhang, Wanru; Liu, Zhongkui; Yang, Xiaoyan. Foxby equivalences associated to strongly Gorenstein modules. Kodai Math. J. 41 (2018), no. 2, 397--412. doi:10.2996/kmj/1530496849. https://projecteuclid.org/euclid.kmj/1530496849