2012/06/15 by Xiaowei Xu, Yang Liu, Xu, Xiaowei +3
Mathematics · #16N60 #16W25 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16N60 #msc:16W25
paper · pdf · doi:10.48550/arxiv.1206.3396
8 pages
arxiv created 2012/06/15 · arxiv updated 2012/06/18
For a ring R with an automorphism σ, an n-additive mapping Δ:R× R×... × R → R is called a skew n-derivation with respect to σ if it is always a σ-derivation of R for each argument. Namely, it is always a σ-derivation of R for the argument being left once n-1 arguments are fixed by n-1 elements in R. In this short note, starting from Brešar Theorems, we prove that a skew n-derivation (n≥ 3) on a semiprime ring R must map into the center of R.