Primary differential nil-algebras exist / G. A. Pogudin. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2014. ? 1. P. 50-53 [Moscow Univ. Math. Bulletin. Vol. 69, N 1, 2014.].

We construct a monomorphism from differential algebra k{x}/[x^m] to Grassmann algebra endowed with the structure of differential algebra. Using this monomorphism, we prove the primality of the k{x}/[x^m] and its algebra of differential polynomials, solve the so-called Ritt problem and give a new proof of integrality of the ideal [x^m].

Key words: differential algebra, algebra of differential polynomials, Ritt problem, prime radical.