Communications of the
Korean Mathematical Society CKMS

For ${\Bbb F}[e^{\pm x}]_{\{\partial\}}$, all the derivations of the evaluation algebra ${\Bbb F}[e^{\pm x}]_{\{\partial\}}$ is found in the paper (see \cite{W}). For $M=\{\partial_1, \partial_1^2 \},$ $Der_{non}({\Bbb F}[e^{\pm x}]_M))$ of the evaluation algebra ${\Bbb F}[e^{\pm x},e^{\pm y}]_M$ is found in the paper (see \cite{C}). For $M=\{\partial_1^2, \partial_2^2 \},$ we find $Der_{non}({\Bbb F}[e^{\pm x}, e^{\pm y}]_M))$ of the evaluation algebra ${\Bbb F}[e^{\pm x},e^{\pm y}]_M$ in this paper.

Keywords: simple, Witt algebra, graded, radical homogeneous equivalent component, order, derivation invariant

MSC numbers: Primary 17B40, 17B56