Inverse limits of automorphisms of truncated polynomials and applications related to Jacobian conjecture

Hao Chang; Bin Shu; Yu Feng Yao

doi:10.1142/S0219498825501750

Inverse limits of automorphisms of truncated polynomials and applications related to Jacobian conjecture

Hao Chang
, Bin Shu^*
, Yu Feng Yao

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic p. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism ϕ of the polynomial ring k[x1, . . ., xn], if ϕ preserves the maximal ideals, then ϕ is an automorphism.

Original language	English
Article number	2550175
Journal	Journal of Algebra and its Applications
Volume	24
Issue number	7
DOIs	https://doi.org/10.1142/S0219498825501750
State	Published - 1 May 2025

Keywords

Jacobian condition
Jacobian conjecture
Jacobian matrix

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10.1142/S0219498825501750

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title = "Inverse limits of automorphisms of truncated polynomials and applications related to Jacobian conjecture",

abstract = "In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic p. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism ϕ of the polynomial ring k[x1, . . ., xn], if ϕ preserves the maximal ideals, then ϕ is an automorphism.",

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AU - Chang, Hao

AU - Shu, Bin

AU - Yao, Yu Feng

N1 - Publisher Copyright: © World Scientific Publishing Company.

PY - 2025/5/1

Y1 - 2025/5/1

N2 - In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic p. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism ϕ of the polynomial ring k[x1, . . ., xn], if ϕ preserves the maximal ideals, then ϕ is an automorphism.

AB - In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic p. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism ϕ of the polynomial ring k[x1, . . ., xn], if ϕ preserves the maximal ideals, then ϕ is an automorphism.

KW - Jacobian condition

KW - Jacobian conjecture

KW - Jacobian matrix

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DO - 10.1142/S0219498825501750

M3 - 文章

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JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

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M1 - 2550175

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Inverse limits of automorphisms of truncated polynomials and applications related to Jacobian conjecture

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