Differential algebraic dependence and Novikov dependence

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 criterion of Novikov dependence of a finite system of elements of free Novikov algebras.

Keywords:

• Differential polynomial algebra
• differential algebraic dependence
• free Novikov algebra
• Novikov dependence

Mathematics Subject Classification (2010):

• Primary 12H05
• 17D25
• Secondary 12L05
• 13P10
• 17A50

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The project is partially supported by the grant AP05133009 of MES RK