Generalization of Herstein theorem and its applications to range inclusion problems
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...
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doaj-62ad02a2cc594dfa9f8366927b3330b82020-11-25T02:44:01ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2014-10-0122332232610.1016/j.joems.2013.11.003Generalization of Herstein theorem and its applications to range inclusion problemsShakir Ali0Mohammad Salahuddin Khan1M. Mosa Al-Shomrani2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202002, IndiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaLet 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.http://www.sciencedirect.com/science/article/pii/S1110256X13001351Prime ringSemiprime ringBanach algebraDerivationJordan derivation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Shakir Ali Mohammad Salahuddin Khan M. Mosa Al-Shomrani |
spellingShingle |
Shakir Ali Mohammad Salahuddin Khan M. Mosa Al-Shomrani Generalization of Herstein theorem and its applications to range inclusion problems Journal of the Egyptian Mathematical Society Prime ring Semiprime ring Banach algebra Derivation Jordan derivation |
author_facet |
Shakir Ali Mohammad Salahuddin Khan M. Mosa Al-Shomrani |
author_sort |
Shakir Ali |
title |
Generalization of Herstein theorem and its applications to range inclusion problems |
title_short |
Generalization of Herstein theorem and its applications to range inclusion problems |
title_full |
Generalization of Herstein theorem and its applications to range inclusion problems |
title_fullStr |
Generalization of Herstein theorem and its applications to range inclusion problems |
title_full_unstemmed |
Generalization of Herstein theorem and its applications to range inclusion problems |
title_sort |
generalization of herstein theorem and its applications to range inclusion problems |
publisher |
SpringerOpen |
series |
Journal of the Egyptian Mathematical Society |
issn |
1110-256X |
publishDate |
2014-10-01 |
description |
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. |
topic |
Prime ring Semiprime ring Banach algebra Derivation Jordan derivation |
url |
http://www.sciencedirect.com/science/article/pii/S1110256X13001351 |
work_keys_str_mv |
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