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.     

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.     

模的r-比较与r-幂比较

本文研究模的r-比较性和r-幂比较性,给出了r-比较性的新刻划,得到了模的r-幂比较结构与其自同态环的r-幂比较性间的关系,证明了如果模M为r-幂比较的则它的任意直和项也是r-幂比较的．对于可分置换环,给出了r-幂比较性与r-比较性间的联系．     

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.     

Comparability and s-Comparability of Modules over Exchange Rings

In this paper, we investigate the comparability structure over exchange rings. It is shown that the subdirect product of an exchange ring with stable range one and an exchange ring satisfying the comparability is also an exchange ring satisfying the comparability. This provides a new class of exchange rings satisfying the comparability. Furthermore, we investigate the s-comparability over exchange rings. This generalizes the corresponding results of Goodearl and Chen. Received November 26, 1999, Accepted February 5, 2001     

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．     

Exchange rings,related comparability and power-substitution

An associative ring R with identity is said to satisfy related comparability provided that for any idempotents e, f ∈ R with e = 1+ ab and f = 1+ba for some a, b ∈R, there exists a central idempotent u ∈R such that ueR is isomorphic to a direct summand of ufR and (1-u)fR is isomorphic to a direct summand of (1 - u)eR In this paper, we investigate the power-cancellation properties of modules over exchange rings satisfying related comparability.     

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.     

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.      

替换环上模的可比较性与s-可比较性

本文讨论替换环上的可比较性结构，　给出一类新的满足可比较性的替换环，　推广了Ｇｏｏｄｅａｒｌ　Ｋ．　Ｒ．和陈焕艮的相应结果．