Displaying similar documents to “Local derivations in polynomial and power series rings”

On the ring of constants for derivations of power series rings in two variables

Leonid Makar-Limanov, Andrzej Nowicki (2001)

Colloquium Mathematicae

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Let k[[x,y]] be the formal power series ring in two variables over a field k of characteristic zero and let d be a nonzero derivation of k[[x,y]]. We prove that if Ker(d) ≠ k then Ker(d) = Ker(δ), where δ is a jacobian derivation of k[[x,y]]. Moreover, Ker(d) is of the form k[[h]] for some h ∈ k[[x,y]].

The Abhyankar-Jung theorem for excellent henselian subrings of formal power series

Krzysztof Jan Nowak (2010)

Annales Polonici Mathematici

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Given an algebraically closed field K of characteristic zero, we prove the Abhyankar-Jung theorem for any excellent henselian ring whose completion is a formal power series ring K[[z]]. In particular, examples include the local rings which form a Weierstrass system over the field K.

The fourteenth problem of Hilbert for polynomial derivations

Andrzej Nowicki (2002)

Banach Center Publications

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We present some facts, observations and remarks concerning the problem of finiteness of the rings of constants for derivations of polynomial rings over a commutative ring k containing the field ℚ of rational numbers.