Linear diophantine equations and local cohomology
Linear diophantine equations and local cohomology
复制标题
DOI：
10.1007/bf01394054
复制
发表时间：
1982-06
影响因子：
3.1
通讯作者：
R. Stanley
中科院分区：
文献类型：
--
作者：
R. Stanley
关于整数系数线性方程组的非负整数解集Ea，我们可以说什么？对于许多目的，如线性规划，这个问题已经得到了充分的回答。然而，当这个问题是从交换代数的优势，许多额外的方面出现。特别地，在一个适当的分次交换环A上，总是有一个与Ea分次模Aa相关联的模，并且人们可以要求关于Aa的标准信息，如它的深度、标准模等。我们将通过显式计算与Aa相关联的局部上同调模H1（A*）的Hilbert函数来获得这些信息（关于A的无关理想），
What can be said about the set Ea of solutions in nonnegative integers to a system of linear equations with integer coefficients? Formany purposes, such asthose oflinear programming, this questionhas been adequately answered.However, when thisquestion is regardedfrom the vantagepoint ofcom mutative algebra, many additional aspects arise. In particular, there is ana turalway toassociate with Eaagraded module Aa (overan appropriate graded commutative ringA\and one canask forsuch standard information aboutAa asitsdepth, canonical module, etc. We will obtain suchinformation by explicitly computingthe Hilbert function ofthe local cohomologymodules Hl (A*) associatedwith Aa (with respectto the irrelevant idealofA) in termsof