Prime differential nilalgebra exists

Abstract

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 $[x^m]$.

4 pages

Cited by in corpus (2)

• Multiplicity structure of the arc space of a fat point
• Combinatorial Differential Algebra of $x^p$