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Quadratic modules over polynomial rings
Quadratic spaces of low rank
Proof of Karoubis theorem
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1-space A-group A-space abelian algebraic group algebraically closed Amer anisotropic assume automorphism central extension closure coefficients cohomology commutative contains Corollary CR structure definition denote derivation differential algebraic differential equations differential field differential ideal differential polynomial differential ring differentially closed fields dimension domain equivalent everywhere defined exact sequence exhibits the rationality exists field of characteristic finite fixed follows formula function G-module Galois group extension group homomorphism Hence homomorphism implies induced injective integral isomorphism isomorphism type kernel Kolchin Lemma Let G Lie algebra linear linearly independent Math matrix maximal ideal module morphism nilpotent nonzero normal subgroup Note prime ideal Proof Let Proposition prove quadratic quasi-compact quasi-primitive rank regular elements representation resp result satisfies Section solution strongly irreducible subfield subset subspace Suppose surjective Theorem theory unimodular unipotent unique valuation vector group vector space zero