| Title:
|
One-sided Gorenstein subcategories (English) |
| Author:
|
Song, Weiling |
| Author:
|
Zhao, Tiwei |
| Author:
|
Huang, Zhaoyong |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
70 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
483-504 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the right (left) Gorenstein subcategory relative to an additive subcategory $\mathscr {C}$ of an abelian category $\mathscr {A}$, and prove that the right Gorenstein subcategory $r\mathcal {G}(\mathscr {C})$ is closed under extensions, kernels of epimorphisms, direct summands and finite direct sums. When $\mathscr {C}$ is self-orthogonal, we give a characterization for objects in $r\mathcal {G}(\mathscr {C})$, and prove that any object in $\mathscr {A}$ with finite $r\mathcal {G}(\mathscr {C})$-projective dimension is isomorphic to a kernel (or a cokernel) of a morphism from an object in $\mathscr {A}$ with finite $\mathscr {C}$-projective dimension to an object in $r\mathcal {G}(\mathscr {C})$. As an application, we obtain a weak Auslander-Buchweitz context related to the kernel of a hereditary cotorsion pair in $\mathscr {A}$ having enough injectives. (English) |
| Keyword:
|
right Gorenstein subcategory |
| Keyword:
|
self-orthogonal subcategory |
| Keyword:
|
relative projective dimension |
| Keyword:
|
cotorsion pair |
| Keyword:
|
kernel |
| Keyword:
|
(weak) Auslander-Buchweitz context |
| MSC:
|
16E10 |
| MSC:
|
18G10 |
| MSC:
|
18G25 |
| idZBL:
|
07217147 |
| idMR:
|
MR4111855 |
| DOI:
|
10.21136/CMJ.2019.0385-18 |
| . |
| Date available:
|
2020-06-17T12:35:30Z |
| Last updated:
|
2022-07-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148241 |
| . |
| Reference:
|
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