Higher-order Image Conjecture for differential operators of polynomial algebras

PUBLICATIONES MATHEMATICAE-DEBRECEN（2022）

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摘要

The interest in images of differential operators of polynomial algebras arose from the research of the Jacobian conjecture. In this paper, we show that the Higher-order Image Conjecture (HIC(n)) holds for all dimensions n ??? 1 in the case of positive characteristic. We also show that HIC(1) holds for a class of differential operators in the case of characteristic zero.

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关键词

Higher-order Image Conjecture, differential operators, Mathieu-Zhao subspaces, Jacobian conjecture

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