Bulletin of the
Korean Mathematical Society
BKMS

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

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Bull. Korean Math. Soc. 2021; 58(1): 217-224

Online first article September 3, 2020      Printed January 31, 2021

https://doi.org/10.4134/BKMS.b200208

Copyright © The Korean Mathematical Society.

Ding injective modules over Frobenius extensions

Zhanping Wang, Pengfei Yang, Ruijie Zhang

Northwest Normal University; Northwest Normal University; Northwest Normal University

Abstract

In this paper, we study Ding injective modules over Frobenius extensions. Let $R\subset A$ be a separable Frobenius extension of rings and $M$ any left $A$-module, it is proved that $M$ is a Ding injective left $A$-module if and only if $M$ is a Ding injective left $R$-module if and only if $A\otimes_{R}M$~($\mathrm{Hom}_{R}(A, M)$) is a Ding injective left $A$-module.

Keywords: Ding injective module, FP-injective module, Frobenius extension

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

Supported by: This work was financially supported by National Natural Science Foundation of China (Grant No. 11561061)

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