Geodesic
Homological dimensions for endomorphism algebras of Gorenstein projective modules
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 675-682 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $A$ be a CM-finite Artin algebra with a Gorenstein-Auslander generator $E$, $M$ be a Gorenstein projective $A$-module and $B = {\rm End}_A M$. We give an upper bound for the finitistic dimension of $B$ in terms of homological data of $M$. Furthermore, if $A$ is $n$-Gorenstein for $2 \leq n \infty $, then we show the global dimension of $B$ is less than or equal to $n$ plus the $B$-projective dimension of ${\rm Hom}_A(M, E).$ As an application, the global dimension of ${\rm End}_A E$ is less than or equal to $n$.
Let $A$ be a CM-finite Artin algebra with a Gorenstein-Auslander generator $E$, $M$ be a Gorenstein projective $A$-module and $B = {\rm End}_A M$. We give an upper bound for the finitistic dimension of $B$ in terms of homological data of $M$. Furthermore, if $A$ is $n$-Gorenstein for $2 \leq n \infty $, then we show the global dimension of $B$ is less than or equal to $n$ plus the $B$-projective dimension of ${\rm Hom}_A(M, E).$ As an application, the global dimension of ${\rm End}_A E$ is less than or equal to $n$.
DOI : 10.21136/CMJ.2024.0199-23
Classification : 16E10, 16G10
Keywords: finitistic dimension; Gorenstein projective module; endomorphism algebra 
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     title = {Homological dimensions for endomorphism algebras of {Gorenstein} projective modules},
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Zhang, Aiping; Lei, Xueping. Homological dimensions for endomorphism algebras of Gorenstein projective modules. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 675-682. doi: 10.21136/CMJ.2024.0199-23

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