The depth of an ideal with a given hilbert function
The depth of an ideal with a given hilbert function
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DOI：
10.1090/s0002-9939-08-09067-9
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发表时间：
2006-08
期刊：
影响因子：
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通讯作者：
S. Murai;T. Hibi
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文献类型：
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作者：
S. Murai;T. Hibi
令A = K[x1，...，xn]表示域K上的n个变量的多项式环，其中每个deg x i = 1。设I是A的齐次理想，I ∈ A，HA/I是商代数A/I的Hilbert函数。给定一个数值函数H：N → N满足H = HA/I对于A的某个齐次理想I，我们记AH为0 ≤ r < n的整数集合，使得存在A的齐次理想I，HA/ I = H，深度A/I = r。将证明，一个人具有A H = {0，1，...，B}，其中0 ≤ B < n，或|啊|= 1。
Let A = K[x 1 ,...,x n ] denote the polynomial ring in n variables over a field K with each deg x i = 1. Let I be a homogeneous ideal of A with I ≠A and H A/I the Hilbert function of the quotient algebra A/I. Given a numerical function H: N → N satisfying H = H A/I for some homogeneous ideal I of A, we write A H for the set of those integers 0 ≤ r < n such that there exists a homogeneous ideal I of A with H A / I = H and with depth A/I = r. It will be proved that one has either A H = {0,1,...,b} for some 0 ≤ b < n or |AH| = 1.