Author | Essen, Arno van den. author |
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Title | Polynomial Automorphisms [electronic resource] : and the Jacobian Conjecture / by Arno van den Essen |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2000 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8440-2 |
Descript | XVIII, 329 p. online resource |
I Methods -- 1. Preliminaries -- 2 Derivations and polynomial automorphisms -- 3 Invertibility criteria and inversion formulae -- 4 Injective morphisms -- 5 The tame automorphism group of a polynomial ring -- 6 Stabilization Methods -- 7 Polynomial maps with nilpotent Jacobian -- II Applications -- 8 Applications of polynomial mappings to dynamical systems -- 9 Group actions -- 10 The Jacobian Conjecture -- III Appendices -- A Some commutative algebra -- A.1 Rings -- A.2 Modules -- A.3 Localization -- A.4 Completions -- A.5 Finiteness conditions and integral extensions -- A.6 The universal coefficients method -- B Some basic results from algebraic geometry -- B.1 Algebraic sets -- B.2 Morphisms of irreducible affine algebraic varieties -- C Some results from Grรถbner basis theory -- C.1 Definitions and basic properties -- C.2 Applications: several algorithms -- D Flatness -- D.1 Flat modules and algebras -- D.2 Flat morphisms between affine algebraic varieties -- E.2 Direct and inverse images -- F Special examples and counterexamples -- Authors Index