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arXiv · 1106.5190

Subalgebras of the polynomial algebra in positive characteristic and the Jacobian

A. V. Gavrilov
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Abstract

Let $k$ be a field of characteristic $p>0$ and $R$ be a subalgebra of $k[X]=k[x_1,...,x_n]$. Let $J(R)$ be the ideal in $k[X]$ defined by $J(R)Ω_{k[X]/k}^n=k[X]Ω_{R/k}^n$. It is shown that if it is a principal ideal then $J(R)^q$ is a subalgebra of $R[x_1^p,...,x_n^p]$, where $q=p^n(p-1)/2$.

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A. V. Gavrilov. 2011-06-26. Subalgebras of the polynomial algebra in positive characteristic and the Jacobian. https://doi.org/10.1142/s0219498811004756

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