Ding injective modules over Frobenius extensions
Bull. Korean Math. Soc.
Published online September 3, 2020
Zhanping Wang, Pengfei Yang, and Ruijie Zhang
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 $M$ be any left $A$-module, it is proved that $M$ is a Ding injective left $A$-module if and only if $M$ is 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 : 13B02, 16G50, 18G25
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