Rings for which general linear forms are exact zero divisors
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911418887962624 |
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| author | Eddings, Ayden Vraciu, Adela |
| author_facet | Eddings, Ayden Vraciu, Adela |
| contents | We investigate the standard graded $k$-algebras over a field $k$ of characteristic zero for which general linear forms are exact zero divisors. We formulate a conjecture regarding the Hilbert function of such rings. We prove our conjecture in the case when the ring is a quotient of a polynomial ring by a monomial idea, and also in the case when the ideal is generated in degree 2 and all but one of the generators are monomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16000 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rings for which general linear forms are exact zero divisors Eddings, Ayden Vraciu, Adela Commutative Algebra 3A02, 13C13 We investigate the standard graded $k$-algebras over a field $k$ of characteristic zero for which general linear forms are exact zero divisors. We formulate a conjecture regarding the Hilbert function of such rings. We prove our conjecture in the case when the ring is a quotient of a polynomial ring by a monomial idea, and also in the case when the ideal is generated in degree 2 and all but one of the generators are monomials. |
| title | Rings for which general linear forms are exact zero divisors |
| topic | Commutative Algebra 3A02, 13C13 |
| url | https://arxiv.org/abs/2407.16000 |