In this paper we prove the following results: (1) For any assosiative differential ring with the unit we introduce a differential analog of the prime-radical and describe it; (2) any maximal differential ideal of a Ritt algebra is prime; (3) The lattice of radical differential ideals satisfies the condition of infinite \cap- distributivity.
HADJIEV, D.; ÇALLIALP, F.; and EDEN, A. (1996) "ON A DIFFERENTIAL ANALOG OF THE PRIME-RADICAL AND PROPERTIES OF THE LATTICE OF RADICAL DIFFERENTIAL IDEALS IN ASSOCIATIVE DIFFERENTIAL RINGS," Turkish Journal of Mathematics: Vol. 20: No. 4, Article 13. Available at: https://journals.tubitak.gov.tr/math/vol20/iss4/13