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

[摘要] 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 >= 2 is an integer, for every integer i is an element of 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 TiUj in the ring k{T}/[TU] equals i + j + 1. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-12-15

[关键词] Differential algebras;Joseph Ritt;Jet schemes;Vertex algebras;Principal subspaces;Free vertex algebras