Differential algebraic dependence and Novikov dependence
Duisengaliyeva B. Umirbaev U.
2021Taylor and Francis Ltd.
Linear and Multilinear Algebra
2021#69Issue 61061 - 1071 pp.
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 criterion of Novikov dependence of a finite system of elements of free Novikov algebras.
differential algebraic dependence , Differential polynomial algebra , free Novikov algebra , Novikov dependence
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L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
Wayne State University, Detroit, MI, United States
Institute of Mathematics and Modeling, Almaty, Kazakhstan
L.N. Gumilyov Eurasian National University
Wayne State University
Institute of Mathematics and Modeling
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