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- W4378499054 abstract "We introduce the concepts of generalized compatible and cocompatible bimodules in order to characterize Gorenstein projective, injective and flat modules over trivial ring extensions. Let $Rltimes M$ be a trivial extension of a ring $R$ by an $R$-$R$-bimodule $M$ such that $M$ is a generalized compatible $R$-$R$-bimodule and $textbf{Z}(R)$ is a generalized compatible $Rltimes M$-$Rltimes M$-bimodule. We prove that $(X,alpha)$ is a Gorenstein projective left $Rltimes M$-module if and only if the sequence $Motimes_R Motimes_R Xstackrel{Motimesalpha}rightarrow Motimes_R Xstackrel{alpha}rightarrow X$ is exact and coker$(alpha)$ is a Gorenstein projective left $R$-module. Analogously, we explicitly characterize Gorenstein injective and flat modules over trivial ring extensions. As an application, we describe Gorenstein projective, injective and flat modules over Morita context rings with zero bimodule homomorphisms." @default.
- W4378499054 created "2023-05-27" @default.
- W4378499054 creator A5024043256 @default.
- W4378499054 date "2023-05-24" @default.
- W4378499054 modified "2023-09-25" @default.
- W4378499054 title "Gorenstein projective, injective and flat modules over trivial ring extensions" @default.
- W4378499054 doi "https://doi.org/10.48550/arxiv.2305.15656" @default.
- W4378499054 hasPublicationYear "2023" @default.
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