A NOTE ON LOCAL COMMUTATORS IN DIVISION RINGS WITH INVOLUTION

被引：3

作者：

Bien, Mai Hoang ^{[1
]}

机构：

[1] Univ Sci Vnuhcm, Fac Math & Comp Sci, 227 Nguyen Van Cu Str,Dist 5, Hcm City, Vietnam

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2019年 / 56卷 / 03期

关键词：

division ring; involution; symmetric element; unitary element; local commutator; ALGEBRAS; SATISFY; UNITS;

D O I：

10.4134/BKMS.b180476

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider a conjecture of I. N. Herstein for local commutators of symmetric elements and unitary elements of division rings. For example, we show that if D is a finite dimensional division ring with involution * and if a is an element of D* = D\{0} such that local commutators axa(-1) x(-1) at a are radical over the center F of D for every x is an element of D* with x* = x, then either a is an element of F or dim(F) D = 4.

引用

页码：659 / 666

页数：8

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