On sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908415996985344 |
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| author | Linh, Nguyen Xuan Nhan, Le Thanh |
| author_facet | Linh, Nguyen Xuan Nhan, Le Thanh |
| contents | We introduce the notions of sequential sequence and sequential f-sequence in order to characterize sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules. Let R be a Noetherian local ring and M a finitely generated R-module. We show that M is sequentially Cohen-Macaulay (resp. sequentially generalized Cohen-Macaulay) if and only if there exists a system of parameters of M that is an M- sequential sequence (resp. each generalized regular sequence s.o.p of M is an M-sequential f-sequence) and R/AnnR(M) is a quotient of a Cohen-Macaulay local ring. As an application, we give new characterizations of Cohen-Macaulay modules and generalized Cohen-Macaulay modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules Linh, Nguyen Xuan Nhan, Le Thanh Commutative Algebra 13E05, 13C14, 13D45 We introduce the notions of sequential sequence and sequential f-sequence in order to characterize sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules. Let R be a Noetherian local ring and M a finitely generated R-module. We show that M is sequentially Cohen-Macaulay (resp. sequentially generalized Cohen-Macaulay) if and only if there exists a system of parameters of M that is an M- sequential sequence (resp. each generalized regular sequence s.o.p of M is an M-sequential f-sequence) and R/AnnR(M) is a quotient of a Cohen-Macaulay local ring. As an application, we give new characterizations of Cohen-Macaulay modules and generalized Cohen-Macaulay modules. |
| title | On sequentially Cohen-Macaulay modules and sequentially generalized Cohen-Macaulay modules |
| topic | Commutative Algebra 13E05, 13C14, 13D45 |
| url | https://arxiv.org/abs/2506.17717 |