Displaying similar documents to “Some results on the kernels of higher derivations on k[x,y] and k(x,y)”

An algorithm to compute the kernel of a derivation up to a certain degree

Stefan Maubach (2001)

Annales Polonici Mathematici

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An algorithm is described which computes generators of the kernel of derivations on k[X₁,...,Xₙ] up to a previously given bound. For w-homogeneous derivations it is shown that if the algorithm computes a generating set for the kernel then this set is minimal.

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]].

On derivations of quantales

Qimei Xiao, Wenjun Liu (2016)

Open Mathematics

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A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation. ...

Local derivations in polynomial and power series rings

Janusz Zieliński (2002)

Colloquium Mathematicae

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We give a description of all local derivations (in the Kadison sense) in the polynomial ring in one variable in characteristic two. Moreover, we describe all local derivations in the power series ring in one variable in any characteristic.