A question of Joseph Ritt from the point of view of vertex algebras

Abstract

Let $k$ be a field of characteristic zero. This paper studies a problem proposed by Joseph F. Ritt in 1950. Precisely, we prove that (1) If $p\ge 2$ is an integer, for every integer $i\in \mathbb{N}$, the nilpotency index of the image of $T_i$ in the ring $k\{T\}/[T^p]$ equals $(i+1)p-i$. (2) For every pair of integers $(i,j)$, the nilpotency index of the image of $T_i{U}_j$ in the ring $k\{T\}/[TU]$ equals $i+j+1$.

References in corpus (1)

• Some remarks on associated varieties of vertex operator superalgebras

Cited by in corpus (1)

• Standard monomials and invariant theory for arc spaces III: special linear group