On commutators and nilpotent elements in simple rings

被引：9

作者：

Chebotar, M. ^{[1
]}

Lee, P-H. ^{[2
,3
]}

Puczylowski, E. R. ^{[4
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[2] Natl Taiwan Univ, Dept Math, Taipei 10764, Taiwan

[3] Taipei Off, Natl Ctr Theoret Sci, Taipei, Taiwan

[4] Univ Warsaw, Inst Math, PL-2 Warsaw, Banacha, Poland

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2010年 / 42卷

关键词：

DISTRIBUTIVE RINGS; SUMS;

D O I：

10.1112/blms/bdp089

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a simple ring with nontrivial zero-divisors. It is proved that every commutator in R is a sum of nilpotent elements if R contains nontrivial idempotents, but it is not so if R does not. An example is also given to show that not every commutator in a prime ring with nontrivial idempotents can be expressed as a sum of nilpotent elements.

引用

页码：191 / 194

页数：4

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