Version 1
: Received: 17 July 2018 / Approved: 17 July 2018 / Online: 17 July 2018 (12:04:11 CEST)
How to cite:
Biernat, G.; Lara-Dziembek, S.; Pawlak, E. Contribution to the Jacobian Conjecture: Polynomial Mapping Having Two Zeros at Infinity. Preprints2018, 2018070311. https://doi.org/10.20944/preprints201807.0311.v1
Biernat, G.; Lara-Dziembek, S.; Pawlak, E. Contribution to the Jacobian Conjecture: Polynomial Mapping Having Two Zeros at Infinity. Preprints 2018, 2018070311. https://doi.org/10.20944/preprints201807.0311.v1
Biernat, G.; Lara-Dziembek, S.; Pawlak, E. Contribution to the Jacobian Conjecture: Polynomial Mapping Having Two Zeros at Infinity. Preprints2018, 2018070311. https://doi.org/10.20944/preprints201807.0311.v1
APA Style
Biernat, G., Lara-Dziembek, S., & Pawlak, E. (2018). Contribution to the Jacobian Conjecture: Polynomial Mapping Having Two Zeros at Infinity. Preprints. https://doi.org/10.20944/preprints201807.0311.v1
Chicago/Turabian Style
Biernat, G., Sylwia Lara-Dziembek and Edyta Pawlak. 2018 "Contribution to the Jacobian Conjecture: Polynomial Mapping Having Two Zeros at Infinity" Preprints. https://doi.org/10.20944/preprints201807.0311.v1
Abstract
This article contains the theorems concerning the algebraic dependence of polynomial mappings with the constant Jacobian having two zeros at infinity. The work is related to the issues of the classical Jacobian Conjecture. This hypothesis affirm that the polynomial mapping of two complex variables with constant non-zero Jacobian is invertible. The Jacobian Conjecture is equivalent to the fact that polynomial mappings with constant non-zero Jacobian do not have two zeros at infinity, therefore it is equivalent to the two theorems given in the work. The proofs of these theorems proceeds by induction.
Keywords
Zeros at infinity, Jacobian Conjecture
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
