- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 A note on local commutators in division rings with involution Bull. Korean Math. Soc. 2019 Vol. 56, No. 3, 659-666 https://doi.org/10.4134/BKMS.b180476Published online May 31, 2019 Mai Hoang Bien University of Science-VNUHCM 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 $a\in D^*=D\backslash\{0\}$ 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 $\dim_{F}D= 4$. Keywords : division ring, involution, symmetric element, unitary element, local commutator MSC numbers : 16K20, 16R50 Downloads: Full-text PDF   Full-text HTML