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Jacobian conjecture

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In mathematics, the Jacobian conjecture was a conjecture concerning polynomials in several variables. It states that if a polynomial function from an n-dimensional space to itself has a Jacobian determinant which is a non-zero constant, then the function has a polynomial inverse. The conjecture was first stated for two variables by Ludwig Kraus in 1884 and then stated in full generality in 1939 by Ott-Heinrich Keller. It was subsequently widely publicized by Shreeram Abhyankar, as an example of a difficult question in algebraic geometry that can be understood using little beyond a knowledge of calculus.

Jacobian conjecture - Wikipedia Jump to content From Wikipedia, the free encyclopedia Disproven conjecture in math N > 2</math>"},"implied by":{"wt":""},"equivalent to":{"wt":"[[Dixmier conjecture]]"},"generalizations":{"wt":""},"consequences":{"wt":""}},"i":0}}]}'> Jacobian conjecture Field Algebraic geometry Conjectured by Ott-Heinrich Keller Conjectured in 1939 Open problem Counterexample found in 2026 for 2"}}'> 2}"> N > 2 {\displaystyle N>2} 2}"/> Equivalent to Dixmier conjecture In mathematics , the Jacobian conjecture is a disproven conjecture [ a ] concerning polynomials in several var

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