Abstract:
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.
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