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http://dx.doi.org/10.4134/BKMS.2013.50.6.1863

SKEW n-DERIVATIONS ON SEMIPRIME RINGS  

Xu, Xiaowei (College of Mathematics Jilin University)
Liu, Yang (College of Mathematics Jilin University)
Zhang, Wei (College of Mathematics Jilin University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.6, 2013 , pp. 1863-1871 More about this Journal
Abstract
For a ring R with an automorphism ${\sigma}$, an n-additive mapping ${\Delta}:R{\times}R{\times}{\cdots}{\times}R{\rightarrow}R$ is called a skew n-derivation with respect to ${\sigma}$ if it is always a ${\sigma}$-derivation of R for each argument. Namely, if n - 1 of the arguments are fixed, then ${\Delta}$ is a ${\sigma}$-derivation on the remaining argument. In this short note, from Bre$\check{s}$ar Theorems, we prove that a skew n-derivation ($n{\geq}3$) on a semiprime ring R must map into the center of R.
Keywords
prime ring; semiprime ring; biderivation; n-derivation; skew n-derivation;
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