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arXiv · 2009.04615

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

Tomoyuki Arakawa·Kazuya Kawasetsu·Julien Sebag
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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 $p\geq 2$ 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 $T_iU_j$ in the ring $k\{T\}/[TU]$ equals $i+j+1$.

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Tomoyuki Arakawa, Kazuya Kawasetsu, Julien Sebag. 2020-09-10. A question of Joseph Ritt from the point of view of vertex algebras. https://arxiv.org/abs/2009.04615

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