Higher-dimensional Teter rings via the canonical trace
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918289770283008 |
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| author | Miyashita, Sora Ozaki, Taiga |
| author_facet | Miyashita, Sora Ozaki, Taiga |
| contents | We study Puthenpurakal's higher-dimensional Teter rings via the canonical trace ideal. We give a sufficient criterion for Teterness and show that, in the standard graded case, it is also necessary, yielding a characterization. Consequently, several nearly Gorenstein families are Teter; moreover, under certain hypotheses, the Cohen--Macaulay type of nearly Gorenstein rings is bounded by the codimension. We also analyze Teterness for fiber products, Veronese subrings, and numerical semigroup rings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_06761 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-dimensional Teter rings via the canonical trace Miyashita, Sora Ozaki, Taiga Commutative Algebra Primary 13H10, 13A02, Secondary 05E40 We study Puthenpurakal's higher-dimensional Teter rings via the canonical trace ideal. We give a sufficient criterion for Teterness and show that, in the standard graded case, it is also necessary, yielding a characterization. Consequently, several nearly Gorenstein families are Teter; moreover, under certain hypotheses, the Cohen--Macaulay type of nearly Gorenstein rings is bounded by the codimension. We also analyze Teterness for fiber products, Veronese subrings, and numerical semigroup rings. |
| title | Higher-dimensional Teter rings via the canonical trace |
| topic | Commutative Algebra Primary 13H10, 13A02, Secondary 05E40 |
| url | https://arxiv.org/abs/2512.06761 |