Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
483517 | Journal of the Egyptian Mathematical Society | 2014 | 5 Pages |
Abstract
Let R be an associative ring. An additive mapping d:R→Rd:R→R is called a Jordan derivation if d(x2)=d(x)x+xd(x)d(x2)=d(x)x+xd(x) holds for all x∈Rx∈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[d(xm),g(yn)]=0 for all x,y∈Rx,y∈R or d(xm)∘g(yn)=0d(xm)∘g(yn)=0 for all x,y∈Rx,y∈R, where m⩾1m⩾1 and n⩾1n⩾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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Shakir Ali, Mohammad Salahuddin Khan, M. Mosa Al-Shomrani,