极小单项理想与线性分解
交换代数
2007-05-23 v2 组合数学
摘要
极小单项理想是组合最简单的单项理想，其 lcm 格等于给定的有限原子格 。该极小理想继承了任何 lcm 格也等于 的理想 的许多良好性质，例如 Cohen-Macaulay 性质以及具有线性分解的对偶性质。反之，任何具有线性分解的理想都被证明是（本质上）极小的。
引用
@article{arxiv.math/0511032,
title = {Minimal monomial ideals and linear resolutions},
author = {Jeffry Phan},
journal= {arXiv preprint arXiv:math/0511032},
year = {2007}
}
备注
14 pages, 4 figures. 2 corrections have been made: (1) The hypothesis in Proposition 2.6 have been corrected to exclude the boundary complex of a simplex. (2) The labeling of the triangle in Figure 2 has been corrected