On a conjecture of Vukman

Qing Deng

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-4

Abstract:

Let R be a ring A bi-additive symmetric mapping d : R × R → R is called a symmetric bi-derivation if, for any fixed y ∈ R , the mapping x → D ( x , y ) is a derivation. The purpose of this paper is to prove the following conjecture of Vukman.

Let R be a noncommutative prime ring with suitable characteristic restrictions, and let D : R × R → R and f : x → D ( x , x ) be a symmetric bi-derivation and its trace, respectively. Suppose that f n ( x ) ∈ Z ( R ) for all x ∈ R , where f k + 1 ( x ) = [ f k ( x ) , x ] for k ≥ 1 and f 1 ( x ) = f ( x ) , then D = 0 .

Date: 1997
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/20/264516.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/20/264516.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:264516

DOI: 10.1155/S0161171297000355

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().