Bulletin of the
Korean Mathematical Society BKMS

We define the non-associative algebra $\overline {W(n,m,m+s)}$ and we show that it is simple. We find the non-associative algebra automorphism group ${\rm Aut}_{non}(\overline {W(1,0,0)} )$ of $\overline {W(1,0,0)} .$ Also we find that any derivation of $\overline {W(1,0,0)}$ is a scalar derivation in this paper.

Keywords: simple, non-associative algebra, right identity, annihilator, Jacobian conjecture, derivation

MSC numbers: Primary 17B40, 17B56