Generalization of Herstein theorem and its applications to range inclusion problems | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 22, Issue 3, October 2014, Pages 322-326 PDF (419.35 K) | ||
| Authors | ||
| Shakir Ali1; Mohammad Salahuddin Khan1; M. Mosa Al-Shomrani2 | ||
| 1Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India | ||
| 2Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia | ||
| Abstract | ||
| Let R be an associative ring. An additive mapping d : R ! R is called a Jordan derivation if dðx2Þ ¼ dðxÞx þ xdðxÞ holds for all x 2 R. The objective of the present paper is to characterize a prime ring R which admits Jordan derivations d and g such that ½dðxmÞ; gðynÞ ¼ 0 for all x; y 2 R or dðxmÞ gðynÞ ¼ 0 for all x; y 2 R, where m P 1 and n P 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. | ||
| Keywords | ||
| Prime ring; Semiprime ring; Banach algebra; Derivation; Jordan derivation | ||
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