SKEW DERIVATIONS AND ENGEL CONDITIONS

被引：12

作者：

Lanski, Charles ^{[1
]}

机构：

[1] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA

来源：

COMMUNICATIONS IN ALGEBRA | 2014年 / 42卷 / 01期

关键词：

Automorphism; Differential identity; Engel polynomial; Prime ring; Skew derivation; Primary; 16W25; Secondary; 16N60; 16W10; 16R50; PRIME-RINGS; DIFFERENTIAL IDENTITIES; POLYNOMIAL IDENTITY; IDEALS;

D O I：

10.1080/00927872.2012.707719

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that for a nonzero derivation d of a prime ring R, if a nonzero ideal I of R satisfies the Engel-type identity [[...[[d(x(0)(k) ), x(1)(k) ], x(2)(k) ],...], x(n)(k) ], then R is commutative. Here we extend this result to a skew derivation of R for a Lie ideal I, which has an immediate corollary that replaces d by an automorphism of R. A related result in two variables is obtained for d a (, phi)-derivation.

引用

页码：139 / 152

页数：14

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