Article
| Title: | Homological dimensions for endomorphism algebras of Gorenstein projective modules (English) |
| Author: | Zhang, Aiping |
| Author: | Lei, Xueping |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 3 |
| Year: | 2024 |
| Pages: | 675-682 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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 $n$. (English) |
| Keyword: | finitistic dimension |
| Keyword: | Gorenstein projective module |
| Keyword: | endomorphism algebra |
| MSC: | 16E10 |
| MSC: | 16G10 |
| DOI: | 10.21136/CMJ.2024.0199-23 |
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| Date available: | 2024-10-03T12:32:49Z |
| Last updated: | 2024-10-04 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152574 |
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