2020/01/02 by Duisengalieva, Bibinur, Umirbaev, Ualbai
#12H05 #17D25 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2001.00383
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.