Jordan Higher Derivable Mappings on Rings. (18th November 2014)

• Record Type: Journal Article
• Authors: Ashraf, Mohammad; Parveen, Nazia
• Other Names: You Hong Academic Editor.
• Is Part Of: Algebra. Volume 2014(2014)
• Publication Date: 2014-11-18
• Subjects: Algebra -- Periodicals; Algebra; Electronic journals; Periodicals; 512.005
• DOI: 10.1155/2014/672387
• Languages: English
• ISSNs: 2314-4106

Abstract

Abstract : Let R be a ring. We say that a family of maps D = { d n } n ∈ N is a Jordan higher derivable map (without assumption of additivity) on R if d 0 = I R (the identity map on R ) and d n ( a b + b a ) = ∑ p + q = n ‍ d p ( a ) d q ( b ) + ∑ p + q = n ‍ d p ( b ) d q ( a ) hold for all a, b ∈ R and for each n ∈ N . In this paper, we show that every Jordan higher derivable map on a ring under certain assumptions becomes a higher derivation. As its application, we get that every Jordan higher derivable map on Banach algebra is an additive higher derivation.