Open AccessGeneralization of Herstein theorem and its applications to range inclusion problems
Author(s) -
Shakir Ali,
M. S. Khan,
M. M. Al-Shomrani
Publication year - 2014
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.11.003
Subject(s) - mathematics , generalization , ring (chemistry) , prime (order theory) , prime ring , algebraic number , associative property , pure mathematics , range (aeronautics) , discrete mathematics , combinatorics , algebra over a field , mathematical analysis , chemistry , materials science , organic chemistry , composite material
Let R be an associative ring. An additive mapping d:R→R is called a Jordan derivation if d(x2)=d(x)x+xd(x) holds for all x∈R. The objective of the present paper is to characterize a prime ring R which admits Jordan derivations d and g such that [d(xm),g(yn)]=0 for all x,y∈R or d(xm)∘g(yn)=0 for all x,y∈R, where m⩾1 and n⩾1 are some fixed integers. This partially extended Herstein’s result in [6, Theorem 2], to the case of (semi)prime ring involving pair of Jordan derivations. Finally, we apply these purely algebraic results to obtain a range inclusion result of continuous linear Jordan derivations on Banach algebras