Invertibility of Polynomials in Differential Algebra

Recent improvements in the decomposition of a radical differential ideal into the intersection of radical differential ideals with specific properties (for example, regular, characteristic, satured, or prime) depend on various notion of invertibility. I'll present a unified treatment based on the works of Aubry, Boulier, Bouziane, Hubert, Kandri-Rody, Sadik, and others.