Necessary and sufficient conditions and special cases of Drużkowski matrices

Yan Tian; Yan Tian

doi:10.3934/math.2026465

AIMS Mathematics

2026, Volume 11, Issue 4: 11322-11331. doi: 10.3934/math.2026465

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Research article

Necessary and sufficient conditions and special cases of Drużkowski matrices

Yan Tian ^,

School of Mathematics, Liaoning Normal University, Dalian 116029, China

Received: 05 February 2026 Revised: 17 March 2026 Accepted: 10 April 2026 Published: 22 April 2026
MSC : 13F20, 14R15

Drużkowski maps play a signiﬁcant role in the study of the Jacobian conjecture. To investigate Drużkowski maps, we identified more Drużkowski matrices via quasi-D-nilpotent matrices, and then studied the corresponding Drużkowski maps. Some necessary and sufficient conditions in which quasi-D-nilpotent matrices were Drużkowski matrices were given. In addition, several classes of special Drużkowski matrices were characterized.
- Drużkowski matrix,
- Jacobian conjecture,
- quasi-D-nilpotent matrix
Citation: Yan Tian. Necessary and sufficient conditions and special cases of Drużkowski matrices[J]. AIMS Mathematics, 2026, 11(4): 11322-11331. doi: 10.3934/math.2026465

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Abstract

Drużkowski maps play a signiﬁcant role in the study of the Jacobian conjecture. To investigate Drużkowski maps, we identified more Drużkowski matrices via quasi-D-nilpotent matrices, and then studied the corresponding Drużkowski maps. Some necessary and sufficient conditions in which quasi-D-nilpotent matrices were Drużkowski matrices were given. In addition, several classes of special Drużkowski matrices were characterized.

References

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