When do pseudo-Gorenstein rings become Gorenstein?
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916808333721600 |
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| author | Miyashita, Sora |
| author_facet | Miyashita, Sora |
| contents | We discuss the relationship between the trace ideal of the canonical module and pseudo-Gorensteinness. In particular, under certain mild assumptions, we show that every pseudo-Gorenstein nearly Gorenstein graded domain is Gorenstein. As an application, we clarify the relationships among nearly Gorensteinness, almost Gorensteinness, and levelness -- notions that generalize Gorensteinness -- in the context of standard graded domains. Moreover, we give a method for constructing quasi-Gorenstein rings by taking a Veronese subalgebra of certain Noetherian graded rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01133 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When do pseudo-Gorenstein rings become Gorenstein? Miyashita, Sora Commutative Algebra Primary 13H10, 13A02, Secondary 05E40 We discuss the relationship between the trace ideal of the canonical module and pseudo-Gorensteinness. In particular, under certain mild assumptions, we show that every pseudo-Gorenstein nearly Gorenstein graded domain is Gorenstein. As an application, we clarify the relationships among nearly Gorensteinness, almost Gorensteinness, and levelness -- notions that generalize Gorensteinness -- in the context of standard graded domains. Moreover, we give a method for constructing quasi-Gorenstein rings by taking a Veronese subalgebra of certain Noetherian graded rings. |
| title | When do pseudo-Gorenstein rings become Gorenstein? |
| topic | Commutative Algebra Primary 13H10, 13A02, Secondary 05E40 |
| url | https://arxiv.org/abs/2502.01133 |