Lyubeznik's Resolution and Rooted Complexes

We describe a new family of free resolutions for a monomial ideal I, generalizing Lyubeznik's construction. These resolutions are cellular resolutions supported on the rooted complexes of the lcm-lattice of I. Our resolutions are minimal for the matroid ideal of a finite projective space.     

幂格的素理想和素对偶理想

在文 [1 ]中 ,引入了幂格的概念 ,并讨论了其相关性质 .本文在此基础上 ,讨论格与其幂格的理想 ,对偶理想的关系 ,以及格与其幂络的素理想 ,素对偶理想的关系 .     

一类整除性定理

本文给出复域上多元多项式环Ｃ［ｘ１，ｘ２，…，ｘｎ］的一类整除性定理，它是［１］中整除定理的直接推广     

Weakly pre-<Emphasis Type=”Italic”>I-</Emphasis>open sets and decomposition of continuity

Summary We establish a general sharp inequality which holds for the family of conformally flat submanifolds in real space form. We show that this inequality does not hold for arbitrary submanifolds in real space forms. We also provide several applications of the inequality.     

弱对偶环

In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, then R is a right AP-injective ring. In addition, some properties of weakly dual rings are given.     

Rings of weak dimension one and syzygetic ideals

We prove that rings of weak dimension one are the rings with all (three-generated) ideals syzygetic. This leads to a characterization of these rings in terms of the André-Quillen homology.

     

BCI-代数中的几种理想

BCI－代数中的理想是一个极其重要的概念，本文引入两类不同的理想，即广义结合理想与拟右交错理想，研究了他们与思想，结合理想，P－理想的关系，并用广义结合理想子代数，刻画了广义结合BCI－代数，指明了拟右交错理想与结合理想的不同之处，用拟右交错理想刻画了拟右交错BCI－代数。     

格序环的一个根的结构

从不同角度刻画了格序环Ｒ的Ｐ－根和ｌ－Ｂ根，并对ｌ－Ｑ根环进行了讨论．揭示了Ｒ及Ｒ上的全矩阵环Ｒｎ的ｌ－Ｑ根，ｌ－Ｑ理想，素ｌ－理想，半素ｌ－理想之间的关系．