Subalgebras of the polynomial algebra in positive characteristic and the Jacobian

Details Subalgebras of the polynomial algebra in positive characteristic and the Jacobian Subalgebras of the polynomial algebra in positive characteristic and the Jacobian

2011-06-26

arxiv.org/abs/1106.5190v1

J.Alg.Appl. 2011

Mathematics

Commutative Algebra

7 pages, LaTex

Scientific paper

10.1142/S0219498811004756

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
$J(R)\Omega_{k[X]/k}^n=k[X]\Omega_{R/k}^n$. 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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