# Differential algebraic dependence and Novikov dependence

@article{Duisengaliyeva2019DifferentialAD, title={Differential algebraic dependence and Novikov dependence}, author={B. Duisengaliyeva and U. Umirbaev}, journal={Linear and Multilinear Algebra}, year={2019}, volume={69}, pages={1061 - 1071} }

ABSTRACT We define an analogue of the Fox derivatives for differential polynomial algebras and give a criterion for differential algebraic dependence of a finite system of elements. In particular, we prove that differential algebraic dependence of a finite set of elements of a differential polynomial algebra over a constructive differential field k of characteristic zero is algorithmically recognizable. Using a representation of free Novikov algebras by differential polynomials we also give a… Expand

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