Geodesic
On the kernels of higher $R$-derivations of~$R[x_1,\dots,x_n]$
Algebra and discrete mathematics, Tome 32 (2021) no. 2, pp. 236-240

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Let $R$ be an integral domain and $A= R[x_1, \dots, x_n]$ be the polynomial ring in $n$ variables. In this article, we study the kernel of higher $R$-derivation $D$ of $A$. It is shown that if $R$ is a HCF ring and $\operatorname{tr.deg}_R(A^D) \leq 1$ then $A^D = R[f]$ for some $f\in A$.
Keywords: derivation, higher derivation, kernel of derivation. 
@article{ADM_2021_32_2_a5,
     author = {S. Kour},
     title = {On the kernels of higher $R$-derivations of~$R[x_1,\dots,x_n]$},
     journal = {Algebra and discrete mathematics},
     pages = {236--240},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a5/}
}
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S. Kour. On the kernels of higher $R$-derivations of~$R[x_1,\dots,x_n]$. Algebra and discrete mathematics, Tome 32 (2021) no. 2, pp. 236-240. http://geodesic.mathdoc.fr/item/ADM_2021_32_2_a5/