Homological dimensions for endomorphism algebras of Gorenstein projective modules

Aiping Zhang; Xueping Lei

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 3, page 675-682
  • ISSN: 0011-4642

Abstract

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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 = 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 ≤ n < ∞ , then we show the global dimension of B is less than or equal to n plus the B -projective dimension of Hom A ( M , E ) . As an application, the global dimension of End A E is less than or equal to n .

How to cite

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Zhang, Aiping, and Lei, Xueping. "Homological dimensions for endomorphism algebras of Gorenstein projective modules." Czechoslovak Mathematical Journal 74.3 (2024): 675-682. <http://eudml.org/doc/299305>.

@article{Zhang2024,
abstract = {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 \le 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 $n$.},
author = {Zhang, Aiping, Lei, Xueping},
journal = {Czechoslovak Mathematical Journal},
keywords = {finitistic dimension; Gorenstein projective module; endomorphism algebra},
language = {eng},
number = {3},
pages = {675-682},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Homological dimensions for endomorphism algebras of Gorenstein projective modules},
url = {http://eudml.org/doc/299305},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Zhang, Aiping
AU - Lei, Xueping
TI - Homological dimensions for endomorphism algebras of Gorenstein projective modules
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 3
SP - 675
EP - 682
AB - 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 \le 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 $n$.
LA - eng
KW - finitistic dimension; Gorenstein projective module; endomorphism algebra
UR - http://eudml.org/doc/299305
ER -

References

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