Primary differential nil-algebras do exist

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