环模上的比较结构

本文推广［１］中主要结论,得到了自同态环的。比较性与模的比较结构间的关系．进一步地,我们把环上的比较结构推广到了模上,并证明了模上的比较性是直和分量不变的．最后,给出了环比较与模比较之间的一类等价关系．     

严格r-预不变凸函数

引入了严格r-预不变凸函数的概念,并证明了严格r-预不变凸函数与r-预不变凸函数有关的一个充分条件．同时,讨论得到了严格r-预不变凸性和半严格r-预不变凸性的等价条件．     

r-锥和严格r-锥

引入有限维向量空间的r-锥和严格r-锥的概念,证明了r-锥是一类闭锥,严格r-锥是一类开锥。并且,研究了r-锥和严格r-锥与较多锥、严格较多锥及它们的闭包和内部之间的关系。     

正则环上的幂问题

本文研究了正则环上模的幂消去，得到了幂消去的内直和刻划．建立了正则环上的幂比较结构，从而给出了正则环上幂消去、幂的弱消去以及ｕ－正则性之间的关系     

求首尾和r-循环矩阵的极小多项式的算法

研究了域上首尾和r-循环矩阵，利用多项式环的理想的Groebner基的算法给出了任意域上首尾和r-循环矩阵的极小多项式和公共极小多项式的一种算法.同时给出了这类矩阵逆矩阵的一种求法。     

基于r-凸函数的Choquet积分不等式

本文研究了r-凸函数的Choquet积分的Hadamard不等式和詹森不等式。首先,针对单调r-凸函数,研究了其Choquet积分的类似Hadamard型不等式;接着,分别在扭曲勒贝格测度和非可加测度下,估计了r-凸函数的Choquet积分的上界;最后,在非可加测度是凹的情形下,给出了两个r-凸函数的Choquet积分的詹森不等式,其可用来估计Choquet积分的下界。另外,在扭曲勒贝格测度下,对文中所有结果进行了例证。     

关于r-预不变凸函数的Hadamard型不等式

定义了r-预不变凸函数,给出了关于r-预不变凸函数的Hadamard型不等式.     

r-拟半开L-集和r-拟半闭L-集

在L-fuzzy拓扑空间中引入r-拟半开L-集和r-拟半闭L-集,正则r-拟半开L-集和正则r-拟半闭L-集,同时讨论它们一些性质.     

关于三元r-循环实矩阵及其应用

讨论三元 r-循环实矩阵 ,给出了三元 r-循环实矩阵的行列式和逆矩阵的实表达式 .从而得到r-循环实矩阵的行列式和逆矩阵的实表达式     

r-置换矩阵的一些性质

本文针对正交表和置换群中的置换矩阵问题,提出了r-置换矩阵的概念,研究了其性质,并且给出这类矩阵逆的求法以及利用Hadamard积得出确定方阵为r-置换矩阵的充要条件,对于我们研究和推广置换矩阵有极其重要的意义。     

Exchange环的比较结构

本文得到了相关比较Exchange环上模的替代性,并研究了幂比较Exchange 环上模的结构,进而提供了一类新的相关比较:Exchange环.     

The Comparable Structure of Exchange Rings

We obtain a new substitution for modules over exchange rings satisfying related comparability. Also we investigate the structure of modules over exchange rings satisfying power comparability and provide a new class of exchange rings satisfying related comparability. Received June 1, 1998, Revised November 15, 1999, Accepted June 1, 2000     

Related comparability over exchange rings

It is shown that every exchange ring satisfying related comparability is separative. This yields that related comparability over exchange rings is Morita invariant. Also we investigate pseudosimilarity over exchange rings satisfying related comparability.     

关于RC-正则环（英文）

我们利用related单位正则无刻画了正则环的比较结构，进而把文[2]定理中的related单位元推广到了related单位正则无，并给出了RC－正则环的一个局部特征．     

On Regular Rings Satisfying Almost Comparability

In this article, we study regular rings satisfying almost comparability. We first show that, for regular rings, almost comparability is inherited by finitely generated projective modules and finite matrix rings, and, as a main result, we prove that the strict cancellation property holds for the family of all finitely generated projective modules over directly finite regular rings satisfying almost comparability.     

Von Neumann Regular Rings Satisfying Weak Comparability

The notion of weak comparability was first introduced by K.C. O’Meara, to prove that directly finite simple regular rings satisfying weak comparability must be unit-regular. In this paper, we shall treat (non-necessarily simple) regular rings satisfying weak comparability and give some interesting results. We first show that directly finite regular rings satisfying weak comparability are stably finite. Using the result above, we investigate the strict cancellation property and the strict unperforation property for regular rings satisfying weak comparability, and we show that these rings have the strict unperforation property, which means that nA ≺ nB implies A ≺ B for any finitely generated projective modules A, B and any positive integer n.      

Regular Rings Satisfying Generalized Almost Comparability

We study regular rings satisfying generalized almost comparability. First, we determine the forms of regular rings satisfying generalized almost comparability. Next, using the above result, we treat the strict cancellation property and the strict unperforation property for regular rings satisfying generalized almost comparability.     

Exchange环及其比较条件

该文得到了Ｅｘｃｈａｎｇｅ性质的内直和刻画,给出了局部环的一个Ｅｘｃｈａｎｇｅ新特征,进一步地研究了Ｅｘｃｈａｎｇｅ环上相关比较结构．