An Engel condition with an additive mapping in semiprime rings

Proceedings Mathematical Sciences

Joso Vukman¹  Maja FoÅ¡ner²  Nadeem Ur Rehman³ 

[1] Department of Mathematics, Physics and Mechanics, University of Maribor, Gosposvetska , 000 Maribor, Slovenia$$;Faculty of Logistics, University of Maribor, Mariborska cesta , 000 Celje, Slovenia$$;Department of Mathematics, Aligarh Muslim University, Aligarh 0 00, India$$

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

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

The main purpose of this paper is to prove the following result: Let 𝑛 > 1 be a fixed integer, let 𝑅 be a 𝑛!-torsion free semiprime ring, and let $f : R → R$ 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* algebra) is semiprime, this purely algebraic result might be of some interest from functional analysis point of view.

【 授权许可】

Unknown