A question of Joseph Ritt from the point of view of vertex algebras
| Autor: | Arakawa, Tomoyuki, Kawasetsu, Kazuya, Sebag, Julien |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $i+j+1$. |
| Databáze: | arXiv |
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