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- W4299928859 abstract "Auslander-Reiten duality for module categories is generalized to some sufficiently nice subcategories. In particular, our consideration works for $mathcal{P}^{<infty}(Lambda)$, the subcategory consisting of finitely generated modules with finite projective dimension over an artin algebra $Lambda$, and also, the subcategory of Gorenstein projectove modules of $rm{mod}mbox{-}Lambda$, denoted by $rm{Gprj}mbox{-}Lambda$. In this paper, we give a method to compute the Auslander-Reiten translation in $mathcal{P}^{<infty}(Lambda)$ whenever $Lambda$ is a $1$-Gorenstein algebra. In addition, we characterize when the Auslander-Reiten translation in $rm{Gprj}mbox{-}Lambda$ is the first syzygy and provide many algebras having such property." @default.
- W4299928859 created "2022-10-03" @default.
- W4299928859 creator A5047826494 @default.
- W4299928859 date "2017-05-18" @default.
- W4299928859 modified "2023-09-26" @default.
- W4299928859 title "Auslander-Reiten duality for subcategories" @default.
- W4299928859 doi "https://doi.org/10.48550/arxiv.1705.06684" @default.
- W4299928859 hasPublicationYear "2017" @default.
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