一般线性形式是精确零除数的环

arXiv - MATH - Commutative Algebra Pub Date : 2024-07-22 DOI:arxiv-2407.16000

Ayden Eddings, Adela Vraciu

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引用次数: 0

摘要

我们研究了一般线性形式为精确零除数的特征为零的域 $k$ 上的标准分级 $k$ 算法。我们提出了关于这类环的希尔伯特函数的猜想。我们证明了在多项式环的商是单项式思想的情况下的猜想，也证明了在理想生成度为 2 且除一个生成子外所有生成子都是单项式的情况下的猜想。

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Rings for which general linear forms are exact zero divisors

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.

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arXiv - MATH - Commutative Algebra

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