Structure of modules stably annihilated by a fixed ideal
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911116524781568 |
|---|---|
| author | Mifune, Yuki |
| author_facet | Mifune, Yuki |
| contents | Let $R$ be a commutative noetherian ring, and denote by $\operatorname{mod} R$ the category of finitely generated $R$-modules. In this paper, for an ideal $I$ of $R$, we introduce the full subcategory $\operatorname{mod}_{I}(R)$ of $\operatorname{mod} R$ consisting of modules whose stable annihilators contain $I$, and we investigate its structure. As an application, we explore the syzygy category of maximal Cohen--Macaulay $R$-modules, extending a theorem of Dey and Liu from the Gorenstein case to the Cohen--Macaulay case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structure of modules stably annihilated by a fixed ideal Mifune, Yuki Commutative Algebra Representation Theory 13C14, 13C60 Let $R$ be a commutative noetherian ring, and denote by $\operatorname{mod} R$ the category of finitely generated $R$-modules. In this paper, for an ideal $I$ of $R$, we introduce the full subcategory $\operatorname{mod}_{I}(R)$ of $\operatorname{mod} R$ consisting of modules whose stable annihilators contain $I$, and we investigate its structure. As an application, we explore the syzygy category of maximal Cohen--Macaulay $R$-modules, extending a theorem of Dey and Liu from the Gorenstein case to the Cohen--Macaulay case. |
| title | Structure of modules stably annihilated by a fixed ideal |
| topic | Commutative Algebra Representation Theory 13C14, 13C60 |
| url | https://arxiv.org/abs/2508.16137 |