论文标题
在维度三中减少主要理想数量的界限
Bounds for the reduction number of primary ideal in dimension three
论文作者
论文摘要
令$（R，\ Mathfrak {M}）$为Cohen-Macaulay dimension $ d \ geq 3 $和$ i $ an $ a $ \ mathfrak {m} $ - $ r $的主要理想。让$ r_j（i）$是$ i $的减少$ i $的减少$ j $ $ i $。假设深度$ g（i）\ geq d-3 $。我们证明$ r_j（i）\ leq e_1（i）-e_0（i）+λ（r/i）+1+（e_2（i）-1）e_2（i）e_2（i）-e_3（i）$，其中$ e_i（i）$是希尔伯特系数。假设$ d = 3 $和深度$ g（i^t）> 0 $对于某些$ t \ geq 1 $。然后，我们证明$ r_j（i）\ leq e_1（i）-e_0（i）+λ（r/i）+t $。
Let $(R,\mathfrak{m})$ be a Cohen-Macaulay local ring of dimension $d\geq 3$ and $I$ an $\mathfrak{m}$-primary ideal of $R$. Let $r_J(I)$ be the reduction number of $I$ with respect to a minimal reduction $J$ of $I$. Suppose depth $G(I)\geq d-3$. We prove that $r_J(I)\leq e_1(I)-e_0(I)+λ(R/I)+1+(e_2(I)-1)e_2(I)-e_3(I)$, where $e_i(I)$ are Hilbert coefficients. Suppose $d=3$ and depth $G(I^t)>0$ for some $t\geq 1$. Then we prove that $r_J(I)\leq e_1(I)-e_0(I)+λ(R/I)+t$.
