SKEW n-DERIVATIONS ON SEMIPRIME RINGS

Title & Authors
SKEW n-DERIVATIONS ON SEMIPRIME RINGS
Xu, Xiaowei; Liu, Yang; Zhang, Wei;

Abstract
For a ring R with an automorphism $\small{{\sigma}}$, an n-additive mapping $\small{{\Delta}:R{\times}R{\times}{\cdots}{\times}R{\rightarrow}R}$ is called a skew n-derivation with respect to $\small{{\sigma}}$ if it is always a $\small{{\sigma}}$-derivation of R for each argument. Namely, if n - 1 of the arguments are fixed, then $\small{{\Delta}}$ is a $\small{{\sigma}}$-derivation on the remaining argument. In this short note, from Bre$\small{\check{s}}$ar Theorems, we prove that a skew n-derivation ($\small{n{\geq}3}$) on a semiprime ring R must map into the center of R.
Keywords
prime ring;semiprime ring;biderivation;n-derivation;skew n-derivation;
Language
English
Cited by
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