Number of generators of ideals
Number of generators of ideals
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理想生成器的数量
DOI：
10.1017/s0027763000003640
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发表时间：
1991
影响因子：
0.8
通讯作者：
G. Valla
中科院分区：
文献类型：
--
作者：
J. Elias;L. Robbiano;G. Valla
设I是一个域上多项式环的齐次理想，v(I) I的任何最小基的元素个数，e = e(I) R/I的多重度或次，h = h(I) I的高度或余维，I = indeg (I) J的初始度，即I的非零元素的最小度。本文主要研究I在大类理想上值域时v(I)的界。例如，当I值域于具有预赋余维数和多重性的完美理想集合上以及当I值域于具有预赋余维数，多重性和初始度的完美理想集合上时，我们得到了界。此外，所有的界限都是明确的，因为它们是由合适的理想达到的。现在让我们做一些历史评论。
Let I be a homogeneous ideal of a polynomial ring over a field, v(I) the number of elements of any minimal basis of I, e = e(I) the multiplicity or degree of R/I, h = h(I) the height or codimension of I, i = indeg (I) the initial degree of J, i.e. the minimal degree of non zero elements of I. This paper is mainly devoted to find bounds for v(I) when I ranges over large classes of ideals. For instance we get bounds when I ranges over the set of perfect ideals with preassigned codimension and multiplicity and when I ranges over the set of perfect ideals with preassigned codimension, multiplicity and initial degree. Moreover all the bounds are sharp since they are attained by suitable ideals. Now let us make some historical remarks.