Prime differential nilalgebra exists

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 primality of $k\{x\} / [x^m]$ and its algebra of differential polynomials, solve one of Ritt's problems and give a new proof of integrality of the ideal $[x^m]$.

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