论文标题
从顶点代数的角度来看，约瑟夫·里特的问题
A question of Joseph Ritt from the point of view of vertex algebras
论文作者
论文摘要
令$ k $为特征零字段。本文研究了约瑟夫·F·里特（Joseph F. Ritt）在1950年提出的一个问题。确切地说，我们证明，如果$ p \ geq 2 $是整数，则对于每个整数$ i \ in \ mathbb {n} $，niltotency Index，nilpotency Index，nilpotency Index of Ring $ K \ k \ k \ t_p-i $ k \ i+a的$ t_i $ in Informentiment Informent （2）对于每对整数$（i，j）$，$ t_iu_j $的nilpotency索引$ k \ {t \}/[tu] $等于$ i+i+j+1 $。
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 $i+j+1$.
