纯正半群的几个判定条件

本文给出了一个半群为纯正半君的几个充分条件。     

结合环类中的E-单环

在全部结合环类中，对幂等根Ｅ，定义了Ｅ－单环．本文给出Ｅ－单环的一个刻画．     

满足a+ab=a+b的幂等半环的结构

本文讨论了满足a+ab=a+b的幂等半环的结构,给出这种幂等半环是左零半环的伪强右正规幂等半环,并得出这种幂等半环与环的直积是左环的伪强右正规幂等半环.     

Belman不等式(I)

本文考察不等式：ｔｒ（ＡＢ）^ｍ≤ｔｒ（Ａ^ｍＢ^ｍ），ｍ＝１，２，３，…，其中Ａ，Ｂ为Ｋ阶方阵．证明了当Ａ正定Ｂ对称幂等条件下上述不等式成立．还考察了Ａ，Ｂ为非负矩阵时的情形     

From the sixteenth Hilbert problem to tropical geometry

Hilbert’s problem on the topology of algebraic curves and surfaces (the sixteenth problem from the famous list presented at the second International Congress of Mathematicians in 1900) was difficult to formulate. The way it was formulated made it difficult to anticipate that it has been solved. In the first part of the paper the history of the sixteenth Hilbert problem and its solution is presented. The second part of the paper traces one of the ways in which tropical geometry emerged. This article is based on the 4th Takagi Lectures that the author delivered at Kyoto University on June 21, 2008.     

奇异变换半群中J类的幂乘数

首先给出奇异变换半群中J类的幂乘数的定义,然后讨论奇异变换半群中J类的幂乘数的性质.     

von Neumann regular modules

In this paper, we introduce von Neumann regular modules and give many characterizations of von Neumann regular modules. Further, we investigate the relations between von Neumann regular modules and other classical modules. Finally, we characterize Noetherian von Neumann regular modules.     

幂等矩阵的组合的零度与秩

本文研究了两个幂等矩阵P与Q的组合Ap Bq-Cpq(a≠0,b≠0)的秩.利用矩阵的核子空间及线性空间的同构的有关性质,得到了:当c＝a b时,Ap Bq-Cpq的秩为一个常数,且等于P-Q的秩;当c≠a b时,Ap Bq-Cpq的秩为一个常数,且等于P Q的秩,推广了J. J. Koliha和V. Rakoeeie[3]的结果.     

Further results on the Moore–Penrose invertibility of projectors and its applications

The aim of this article is to investigate new results on the Moore–Penrose invertibility of the products and differences of projectors and generalized projectors. The range relations of projectors and the detailed representations for Moore–Penrose inverses are presented.