Higher dimensional Teter rings
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929684797718528 |
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| author | Puthenpurakal, Tony J. |
| author_facet | Puthenpurakal, Tony J. |
| contents | Let $(A,\mathfrak{m})$ be a complete Cohen-Macaulay local ring. Assume $A$ is not Gorenstein. We say $A$ is a Teter ring if there exists a complete Gorenstein ring $(B,\mathfrak{n})$ with $\dim B = \dim A$ and a surjective map $B \rightarrow A$ with $e(B) - e(A) = 1$ (here $e(A)$ denotes multiplicity of $A$). We give an intrinsic characterization of Teter rings which are domains. We say a Teter ring is a strongly Teter ring if $G(B) = \bigoplus_{i \geq 0}\mathfrak{n}^i/\mathfrak{n}^{i+1}$ is also a Gorenstein ring. We give an intrinsic characterizations of strongly Teter rings which are domains. If $k$ is algebraically closed field of characteristic zero and $R$ is a standard graded Cohen-Macaulay $k$-algebra of finite representation type (and not Gorenstein) then we show that $\widehat{R_\mathfrak{M}}$ is a Teter ring (here $\mathfrak{M}$ is the maximal homogeneous ideal of $R$). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_13526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher dimensional Teter rings Puthenpurakal, Tony J. Commutative Algebra Primary 13H10, Secondary 13A30 Let $(A,\mathfrak{m})$ be a complete Cohen-Macaulay local ring. Assume $A$ is not Gorenstein. We say $A$ is a Teter ring if there exists a complete Gorenstein ring $(B,\mathfrak{n})$ with $\dim B = \dim A$ and a surjective map $B \rightarrow A$ with $e(B) - e(A) = 1$ (here $e(A)$ denotes multiplicity of $A$). We give an intrinsic characterization of Teter rings which are domains. We say a Teter ring is a strongly Teter ring if $G(B) = \bigoplus_{i \geq 0}\mathfrak{n}^i/\mathfrak{n}^{i+1}$ is also a Gorenstein ring. We give an intrinsic characterizations of strongly Teter rings which are domains. If $k$ is algebraically closed field of characteristic zero and $R$ is a standard graded Cohen-Macaulay $k$-algebra of finite representation type (and not Gorenstein) then we show that $\widehat{R_\mathfrak{M}}$ is a Teter ring (here $\mathfrak{M}$ is the maximal homogeneous ideal of $R$). |
| title | Higher dimensional Teter rings |
| topic | Commutative Algebra Primary 13H10, Secondary 13A30 |
| url | https://arxiv.org/abs/2501.13526 |