On the structure of finitely generated modules and the unmixed degrees
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arXiv
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| Format: | Preprint |
| Published: |
2016
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| _version_ | 1866908369441259520 |
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| author | Cuong, Nguyen Tu Quy, Pham Hung |
| author_facet | Cuong, Nguyen Tu Quy, Pham Hung |
| contents | Let $(R, \frak m)$ be a homomorphic image of a Cohen-Macaulay local ring and $M$ a finitely generated $R$-module. We use the splitting of local cohomology to shed a new light on the structure of non-Cohen-Macaulay modules. Namely, we show that every finitely generated $R$-module $M$ is associated by a sequence of invariant modules. This modules sequence expresses the deviation of $M$ with the Cohen-Macaulay property. This result generalizes the unmixed theorem of Cohen-Macaulayness for any finitely generated $R$-module. As an application we construct a new extended degree in sense of Vasconcelos. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1612_07638 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | On the structure of finitely generated modules and the unmixed degrees Cuong, Nguyen Tu Quy, Pham Hung Commutative Algebra 13H10, 13D45, 13H15 Let $(R, \frak m)$ be a homomorphic image of a Cohen-Macaulay local ring and $M$ a finitely generated $R$-module. We use the splitting of local cohomology to shed a new light on the structure of non-Cohen-Macaulay modules. Namely, we show that every finitely generated $R$-module $M$ is associated by a sequence of invariant modules. This modules sequence expresses the deviation of $M$ with the Cohen-Macaulay property. This result generalizes the unmixed theorem of Cohen-Macaulayness for any finitely generated $R$-module. As an application we construct a new extended degree in sense of Vasconcelos. |
| title | On the structure of finitely generated modules and the unmixed degrees |
| topic | Commutative Algebra 13H10, 13D45, 13H15 |
| url | https://arxiv.org/abs/1612.07638 |