A finite universal SAGBI basis for the kernel of a derivation (Q1769140)

This paper is devoted to the study of properties of SAGBI basis (``Sub-algebra Analogue to Gröbner bases for ideals'') for the kernel of a derivation of a polynomials ring. These bases were introduced by \textit{L. Robbiano} and \textit{M. Sweedler} [Lect. Notes Math. 1430, 61--87 (1990; Zbl 0725.13013)] and by \textit{D. Kapur} and \textit{K. Madlener} [in: Computers and mathematics, Proc. Conf., Cambridge/Mass 1--11 (1989; Zbl 0692.13001)]. The authors provide a sufficient condition on derivations for their kernels to have finite universal SAGBI bases, as well as an upper bound of distinct initial algebras of them.