Gröbner $δ$-bases and Gröbner bases for differential operators

Abstract

This paper deals with the notion of Gröbner $δ$-base for some rings of linear differential operators by adapting the works of W. Trinks, A. Assi, M. Insa and F. Pauer. We compare this notion with the one of Gröbner base for such rings. As an application, and following a previous work of A. Assi, we give some results on finiteness and on flatness of finitely generated left modules over these rings.