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exchange rings having ideal-stable range one

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Science China Mathematics 2001年第5期44卷 579-586页

作者：陈焕银李福安 Department of Mathematics Hunan Normal University Changsha China Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this paper, we introduce the notion of the ideal-stable range one condition for exchange rings. Some characterizations for this condition are given. Moreover, we show that, for an exchange ring R, if I is an ideal of R and R has I-stable range one, then every regular square matrix over I is the product of an idempotent matrix and an invertible matrix over R, and admits a diagonal reduction.

关键词： exchange ring stable range condition diagonal reduction.

The Comparable Structure of exchange rings

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Acta Mathematica Sinica,English Series 2002年第1期18卷 89-94页

作者： CHEN Huan Yin QIN Hou Rong Department of Mathematics. Hunan Normal University. Changsha 410006. P. R. China Department of Mathematics. Nanjing University. Nanjing 210093. P. R. China Department of Mathematics Hunan Normal University Changsha P. R. China Department of Mathematics Nanjing University Nanjing P. R. China

We obtaim a new substitution for modules over exchange rings satisfving related compara- bilitv. Also we investigate the structure of modules over exchange rings satisfying power comparability and provide a new class ... 详细信息

关键词： Related comparability Power comparability exchange ring

Comparability and s-Comparability of Modules over exchange rings

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Acta Mathematica Sinica,English Series 2001年第3期17卷 481-488页

作者： Huan Yin CHEN Department of Mathematics,Hunan Normal University,Changsha 410006 P.R.China E-mail:chyzxl@sparc2.hunnu.edu.cnFu An LI Institute of Mathematics,Academy of Mathematics and System Sciences Chinese Academy of Sciences,Beijing 100080,P.R.China E-mail:fal@*** Department of Mathematics Human Normal University Changsha 410006 P. R. China Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy Sciences Beijing 100080 P. R. China

In this paper,we investigate the comparability structure over exchange *** 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 *** provides a new class of exchange rings satisfying the ***,we investigate the s-comparability over exchange *** generalizes the corresponding results of Goodearl and Chen.

关键词： exchange ring Comparability s-comparability

A Note on Elements and Modules over exchange rings

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Communications in Mathematical Research 1999年第2期 115-119页

作者： Chen Huanyin (Department of Mathematics, Hunan Normal University, Changsha, 410006)

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ＬｅｔＲｂｅａｎａｓｓｏｃｉａｔｉｖｅｒｉｎｇｗｉｔｈｉｄｅｎｔｉｔｙ．ＡｒｉｇｈｔＲ－ｍｏｄｕｌｅＡｉｓｓａｉｄｔｏｓａｔｉｓｆｙｆｉｎｉｔｅｅｘｃｈａｎｇｅｐｒｏｐｅｒｔｙｉｆｆｏｒｅｖｅｒｙｒｉｇｈｔＲ－ｍｏｄｕｌｅＫａｎｄａｎｙｔｗｏｄｅｃｏ...

关键词： exchange ring Primitive Factor Weakly P exchange ring

exchange general rings

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Journal of Southeast University(English Edition) 2006年第4期22卷 589-592页

作者：黄青鹤陈建龙东南大学理学院南京210096

The exchange rings without unity, first introduced by Ara, are further investigated. Some new characterizations and properties of exchange general rings are given. For example, a general ring I is exchange if and only if for any left ideal L of I and a^-= a^-2 ∈I/L, there exists w ∈ r. ureg（I） such that w^- = a^-; E（R, I）（ the ideal extension of a ring R by its ideal I） is an exchange ring if and only if R and I are both exchange. Furthermore, it is presented that if I is a two-sided ideal of a unital ring R and I is an exchange general ring, then every central element of I is a clean element in 1.

关键词： exchange ring clean element stable range one ideal extension

On Endomorphism rings of Regular Modulos (Dedicated to Professor Zhou Boxun for his 80'th Birthday)

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Acta Mathematica Sinica,English Series 1998年第3期14卷 385-390页

作者： Wu Tongsuo Department of Applied Mathematics. Shanghai Jiaotong University. Shanghai 200030, China

In this paper. we study the endomorphism rings of regular *** give sufficient conditions on a regular projective module P such that End_R(P) has stable range one.

关键词： Regular projective module Stable range one exchange ring

On π-regularity of General rings

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Communications in Mathematical Research 2010年第4期26卷 313-320页

作者： CHEN WEI-XING CUI SHU-YING School of Mathematics and Information Science Shandong Institute of Business and Technology Yantai 264005

A general ring means an associative ring with or without *** idempotent e in a general ring I is called left (right) semicentral if for every x ∈ I,xe=exe (ex=exe).And I is called semiabelian if every idempotent in I is left or right *** is proved that a semiabelian general ring I is π-regular if and only if the set N (I) of nilpotent elements in I is an ideal of I and I /N (I) is *** follows that if I is a semiabelian general ring and K is an ideal of I,then I is π-regular if and only if both K and I /K are π-*** on this we prove that every semiabelian GVNL-ring is an *** generalize several known results on the relevant *** we give a characterization of a semiabelian GVNL-ring.

关键词： semiabelian ring π-regular ring GVNL-ring exchange ring