Remarks on almost Gorenstein rings
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913206395469824 |
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| author | Endo, Naoki Matsuoka, Naoyuki |
| author_facet | Endo, Naoki Matsuoka, Naoyuki |
| contents | This paper investigates the relation between the almost Gorenstein properties for graded rings and for local rings. Once $R$ is an almost Gorenstein graded ring, the localization $R_M$ of $R$ at the graded maximal ideal $M$ is almost Gorenstein as a local ring. The converse does not hold true in general. However, it does for one-dimensional graded domains with mild conditions, which we clarify in the present paper. We explore the defining ideals of almost Gorenstein numerical semigroup rings as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13479 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Remarks on almost Gorenstein rings Endo, Naoki Matsuoka, Naoyuki Commutative Algebra 13H10, 13A15, 13A02 This paper investigates the relation between the almost Gorenstein properties for graded rings and for local rings. Once $R$ is an almost Gorenstein graded ring, the localization $R_M$ of $R$ at the graded maximal ideal $M$ is almost Gorenstein as a local ring. The converse does not hold true in general. However, it does for one-dimensional graded domains with mild conditions, which we clarify in the present paper. We explore the defining ideals of almost Gorenstein numerical semigroup rings as well. |
| title | Remarks on almost Gorenstein rings |
| topic | Commutative Algebra 13H10, 13A15, 13A02 |
| url | https://arxiv.org/abs/2307.13479 |