Permanental ideals of symmetric matrices
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909602508963840 |
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| author | Chau, Trung |
| author_facet | Chau, Trung |
| contents | In this article, we study the ideal generated by $2\times 2$ permanents of a symmetric matrix. We denote this ideal by $P_2(X)$ where $X$ is a symmetric matrix. We compute a Gröbner basis, dimension, depth, minimal primes, and a primary decomposition of $P_2(X)$. It can be seen that the answer is reliant on whether the characteristic of the base field is two, and thus these ideals constitute a class of ideals whose algebraic properties depend on characteristics of the base field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03367 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Permanental ideals of symmetric matrices Chau, Trung Commutative Algebra Algebraic Geometry 13C05, 13C40, 13P10, 15A15, 05E40 In this article, we study the ideal generated by $2\times 2$ permanents of a symmetric matrix. We denote this ideal by $P_2(X)$ where $X$ is a symmetric matrix. We compute a Gröbner basis, dimension, depth, minimal primes, and a primary decomposition of $P_2(X)$. It can be seen that the answer is reliant on whether the characteristic of the base field is two, and thus these ideals constitute a class of ideals whose algebraic properties depend on characteristics of the base field. |
| title | Permanental ideals of symmetric matrices |
| topic | Commutative Algebra Algebraic Geometry 13C05, 13C40, 13P10, 15A15, 05E40 |
| url | https://arxiv.org/abs/2505.03367 |