Results 21 to 30 of about 25,672 (245)
EQUIVARIANT JACOBIAN CONJECTURE IN DIMENSION TWO
Transformation Groups, 2022 To be published in Transformation ...
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A Survey of Research on Square-Free and Radical Factorizations:from Jacobian-Type Conditions to Ideals in Noncommutative Rings [PDF]
Military Technology and ScienceThis article presents a survey of research on square-free and radical factorizations in rings and monoids, both in the commutativeand noncommutative settings.
Łukasz Matysiak
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Graphs and the Jacobian conjecture
Journal of Pure and Applied Algebra, 2008 From the abstract: It is proven in [\textit{M. de Bondt, A. van den Essen}, Proc. Am. Math. Soc. 133, No.~8, 2201--2205 (2005; Zbl 1073.14077)] that it suffices to study the Jacobian conjecture for maps of the form \(x+\nabla f\), where \(f\) is a homogeneous polynomial of degree \(d=4\).
Essen, A.R.P. van den, Willems, R.M.M.
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, 2023 The Jacobian conjecture involves the map $y= x - V(x)$ where $y, x$ are n-dimensional vectors, $V(x)$ is a symmetric polynomial of degree $d$ for which the Jacobian hypothesis holds: $ e^{Tr \ln(1- V'(x))} =1,\ \forall x$. The conjecture states that the inverse map ($x$ as a function of $y$) is also polynomial.
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UNLIKELY INTERSECTIONS IN FINITE CHARACTERISTIC
Forum of Mathematics, Sigma, 2018 We present a heuristic argument based on Honda–Tate theory against many conjectures in ‘unlikely intersections’ over the algebraic closure of a finite field; notably, we conjecture that every abelian variety of dimension 4 is isogenous to a Jacobian ...
ANANTH N. SHANKAR, JACOB TSIMERMAN
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Nilpotent symmetric Jacobian matrices and the Jacobian Conjecture II
Journal of Pure and Applied Algebra, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bondt, M.C. de, Essen, A.R.P. van den
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Holonomic modules and 1-generation in the Jacobian Conjecture
Comptes Rendus. MathématiqueLet $P_n$ be a polynomial algebra in $n$ indeterminates over a field $K$ of characteristic zero. An endomorphism $\sigma \in \mathrm{End}_K(P_n)$ is called a Jacobian map if its Jacobian is a nonzero scalar.
Bavula, Volodymyr V.
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Recent progress on the Jacobian Conjecture [PDF]
Annales Polonici Mathematici, 2005 In this paper we describe some recent developments concerning the Jacobian Conjecture(JC). First we describe Druzkowski’s result in [6] which asserts that it suffices to study the JC for Druzkowski mappings of the form x + (Ax)∗3 with A = 0. Then we describe the authors’ result of [2] which asserts that it suffices to study the JC for so-called ...
Bondt, M.C. de, Essen, A.R.P. van den
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A new qualitative proof of a result on the real jacobian conjecture
Anais da Academia Brasileira de Ciências, 2015 Let F= (f, g) : R2 → R2be a polynomial map such that det DF(x) is different from zero for all x∈ R2. We assume that the degrees of fand gare equal. We denote by the homogeneous part of higher degree of f and g, respectively.
FRANCISCO BRAUN, JAUME LLIBRE
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