Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2020; 57(6): 1567-1579

Online first article September 4, 2020      Printed November 30, 2020

https://doi.org/10.4134/BKMS.b200056

Copyright © The Korean Mathematical Society.

Gorenstein modules under Frobenius extensions

Fangdi Kong, Dejun Wu

Lanzhou University of Technology; Lanzhou University of Technology

Abstract

Let $R\subset S$ be a Frobenius extension of rings and $M$ a left $S$-module and let $\mathcal{X}$ be a class of left $R$-modules and $\mathcal{Y}$ a class of left $S$-modules. Under some conditions it is proven that $M$ is a $\mathcal{Y}$-Gorenstein left $S$-module if and only if $M$ is an $\mathcal{X}$-Gorenstein left $R$-module if and only if $\tp{S}{M}$ and $\Hom{S}{M}$ are $\mathcal{Y}$-Gorenstein left $S$-modules. This statement extends a known corresponding result. In addition, the situations of Ding modules, Gorenstein AC modules and projectively coresolved Gorenstein flat modules are considered under Frobenius extensions.

Keywords: Frobenius extension, $\mathcal{X}$-Gorenstein module, super finitely presented module, Ding module, PGF-module

MSC numbers: Primary 13B02, 16G50, 18G25

Supported by: This work was financially supported by NSF of China grants 11761047 and 11861043

Stats or Metrics

Share this article on :

Related articles in BKMS

more +