论文标题
相关级过滤环的布克斯鲍姆
Buchsbaumness of the associated graded rings of filtration
论文作者
论文摘要
令$（a，\ mathfrak {m}）$为noetherian dimension $ d> 0 $和$ i $ a $ \ mathcal {i} $的本地环 - $ a $的主要理想。在本文中，我们讨论了一个足够的条件，因为将本地环$ a $的布赫斯鲍姆（Buchsbaumness）传递到相关的过滤环上。令$ \ Mathcal {i} $表示$ i $ good过滤。我们证明，如果$ a $是buchsbaum和i-invariant，$ i（a）$和$ i（g（\ nathcal {i}））$，然后是相关的分级ring $ g（\ mathcal {i}）$是buchsbabaum。作为我们结果的应用，我们在某些希尔伯特系数的边界条件下，指出了Corso的替代证明。
Let $(A,\mathfrak{m})$ be a Noetherian local ring of dimension $d>0$ and $I$ an $\mathcal{I}$-primary ideal of $A$. In this paper, we discuss a sufficient condition, for the Buchsbaumness of the local ring $A$ to be passed onto the associated graded ring of filtration. Let $\mathcal{I}$ denote an $I$-good filtration. We prove that if $A$ is Buchsbaum and the I-invariant, $I(A)$ and $I(G(\mathcal{I}))$, coincide then the associated graded ring $G(\mathcal{I})$ is Buchsbaum. As an application of our result, we indicate an alternative proof of a conjecture, of Corso on certain boundary conditions for Hilbert coefficients.
