单项式理想幂的代数性质

发布时间：2018-03-10 13:51

本文选题：边理想　切入点：无平方因子　出处：《苏州大学》2015年硕士论文　论文类型：学位论文

【摘要】：本文主要分为五部分,前两章分别介绍了文章的研究背景及相关预备知识。令G为一简单图,I为它的边理想。文献[9]中作者证明了定理：Ass(R/I)(?) Ass(R/I2) (?) Ass(R/I3)(?)...。在第三章,本文将给出此定理一个更为简单的证明。令G为一连通图,它只含一个奇圈,且除此之外不含其他圈。第四章着重研究了若I为图G的边理想,Ass(R/It)能在何处达到稳定。第五章证明了无平方单项式理想I为标准挠自由时,其子式也为标准挠自由,同时I具有packing性质。
[Abstract]:This paper is mainly divided into five parts. The first two chapters introduce the research background and related preparatory knowledge of the paper respectively. Let G be a simple graph I as its edge ideal. ) Assan R / I2)? Assan R / I 3? In Chapter 3, we will give a simpler proof of this theorem. Let G be a connected graph, and it contains only one odd cycle. In chapter 4th, we focus on where the edge ideal Assr / I can achieve stability if I is the graph G. Chapter 5th proves that the subform of the square monomial ideal I is the standard torsion freedom when I is the standard torsion freedom. At the same time, I has packing property.
【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O153.3

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