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http://dx.doi.org/10.4134/BKMS.b180476

A NOTE ON LOCAL COMMUTATORS IN DIVISION RINGS WITH INVOLUTION

Bien, Mai Hoang (Faculty of Mathematics and Computer Science University of Science-VNUHCM)

Publication Information

Bulletin of the Korean Mathematical Society / v.56, no.3, 2019 , pp. 659-666 More about this Journal

Abstract

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 $a{\in}D^*=D{\setminus}\{0\}$ 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 ${\dim}_F\;D=4$ .

Keywords

division ring; involution; symmetric element; unitary element; local commutator;

Citations & Related Records

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