• An Engel condition with an additive mapping in semiprime rings

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/124/04/0497-0500

• # Keywords

Prime ring; semiprime ring; additive mapping; derivation; commuting mapping; centralizing mapping; functional identity.

• # Abstract

The main purpose of this paper is to prove the following result: Let $n \gt 1$ be a fixed integer, let 𝑅 be a $n!$-torsion free semiprime ring, and let $f : R \to R$ be an additive mapping satisfying the relation $[f (x), x]_{n} = [[... [[f(x),x],x],...], x] = 0$ for all $x \in R$. In this case $[f(x), x] = 0$ is fulfilled for all $x \in R$. Since any semisimple Banach algebra (for example, $C^{\ast}$ algebra) is semiprime, this purely algebraic result might be of some interest from functional analysis point of view.

• # Author Affiliations

1. Faculty of Logistics, University of Maribor, Mariborska cesta 7, 3000 Celje, Slovenia
2. Department of Mathematics, Aligarh Muslim University, Aligarh 202 002, India
3. Department of Mathematics, Physics and Mechanics, University of Maribor, Gosposvetska 84, 2000 Maribor, Slovenia

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019