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arXiv · 1802.00149

Gorenstein projective dimensions of modules over minimal Auslander-Gorenstein algebras

Shen Li·René Marczinzik·Shunhua Zhang
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Abstract

In this article we investigate the relations between the Gorenstein projective dimensions of $\Lambda$-modules and their socles for minimal n-Auslander-Gorenstein algebras $\Lambda$ in the sense of Iyama and Solberg \cite{IS}. First we give a description of projective-injective $\Lambda$-modules in terms of their socles. Then we prove that a $\Lambda$-module $N$ has Gorenstein projective dimension at most n iff its socle has Gorenstein projective dimension at most n iff $N$ is cogenerated by a projective $\Lambda$-module. Furthermore, we show that minimal n-Auslander-Gorenstein algebras can be characterised by the relations between the Gorenstein projective dimensions of modules and their socles.

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Shen Li, René Marczinzik, Shunhua Zhang. 2018-02-01. Gorenstein projective dimensions of modules over minimal Auslander-Gorenstein algebras. https://arxiv.org/abs/1802.00149

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