Abstract
Let k be a field of characteristic p > 0. We describe all p-homogeneous k-derivations d of k[x, y] such that k[x, y]
d
, the ring of constants with respect to d, is generated, as a k[x
p
,y
p
]-algebra, by a single element. Moreover, we present a characterization of p-homogeneous polynomials f ∈ k[x
1,…, x
n
] for which there exists a p-homogeneous k-derivation d of k[x
1,…, x
n
] such that k[x
1,…, x
n
]
d
= k[,…,
, f].
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