On $n$-derivations

Abstract

In this article, the notion of $n-$derivation is introduced for all integers $ngeq 2$. Although all derivations are $n-$derivations, in general these notions are not equivalent. Some properties of ordinary derivations are investigated for $n-$derivations. Also, we show that under certain mild condition $n-$derivations are derivations.

Keywords

• $n$-derivation
• $n$-homomorphism
• Banach algebra