A note on local commutators in division rings with involution

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 $\star$ and if $a\in D^*=D\backslash\{0\}$ such that local commutators...

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2019, 56(3), , pp.659-666
Main Author: Mai Hoang Bien
Format: Article
Language:English
Subjects:
수학
Online Access:Get full text
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Summary: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 $\star$ and if $a\in D^*=D\backslash\{0\}$ such that local commutators $axa^{-1}x^{-1}$ at $a$ are radical over the center $F$ of $D$ for every $x\in D^*$ with $x^\star=x$, then either $a\in F$ or $\dim_{F}D= 4$. KCI Citation Count: 3
ISSN:1015-8634
2234-3016
DOI:10.4134/BKMS.b180476