The strong Rees property of powers of the maximal ideal and Takahashi-Dao's question,
The strong Rees property of powers of the maximal ideal and Takahashi-Dao's question,
复制标题
最大理想的力量的强里斯性质和高桥道的问题，
DOI：
10.1016/j.jalgebra.2018.07.028
复制
发表时间：
2021
影响因子：
0.9
通讯作者：
K. Watanabe. K. YOshida
中科院分区：
文献类型：
--
作者：
T. Puthenpurakal;K. Watanabe. K. YOshida
本文引入了Noether局部环的m-准素理想的强Rees性质的概念，证明了极大理想m的任意幂都有强Rees性质，如果m的分次环G的深度G≥ 2.作为它的应用，我们刻画了二维优良正规局域，使m是一个p g-理想。最后，我们问什么m-主要理想有SRP和国家的猜想，其特点的情况下，当m-n是唯一的理想有SRP。
In this paper, we introduce the notion of the strong Rees property (SRP) for m-primary ideals of a Noetherian local ring and prove that any power of the maximal ideal m has its property if the associated graded ring G of m satisfies depth G≥ 2. As its application, we characterize two-dimensional excellent normal local domains so that m is a p g-ideal. Finally we ask what m-primary ideals have SRP and state a conjecture which characterizes the case when m n are the only ideals which have SRP.