Linear derivations with rings of constants generated by linear forms
Volume 113 / 2008
Colloquium Mathematicum 113 (2008), 279-286
MSC: Primary 12H05; Secondary 13N15.
DOI: 10.4064/cm113-2-9
Abstract
Let $k$ be a field. We describe all linear derivations $d$ of the polynomial algebra $k[x_1,\dots,x_m]$ such that the algebra of constants with respect to $d$ is generated by linear forms: (a) over $k$ in the case of $\mbox{char}\,k=0$, (b) over $k[x_1^p,\dots,x_m^p]$ in the case of $\mbox{char}\,k=p>0$.
