论文标题
autour de ladécompositiondesalgèbresd'Exposant 2 sur les Extensions Multiquadratiques
Autour de la décomposition des algèbres d'exposant 2 sur les extensions multiquadratiques
论文作者
论文摘要
对于指数的中央简单代数，特征性$ 2 $和2 $ 2 $的$ 2 $的代数$ 2 $ - 等于$ 2 $，我们研究了基本场的某些多QuipaiDratic Extensions的调整分解。最多$ 4 $，将几种显着的属性扩展到可分离性程度的多QuaDratic扩展。我们还扩展到Elman-Lam-tignol-Wadsworth的特征$ 2 $，通过构建指数$ 2 $和$ 8 $的代数，其中包含可分离的三叶酸扩展，但没有承认对此扩展的适应性分解。作为应用程序，我们给出了可分离生物段扩展的非偏见的基本证明。
For central simple algebras of exponent $2$ over fields of characteristic $2$ and $2$-cohomological dimension equal to $2$, we study the adapted decomposition to some multiquadratic extensions of the base field. Several remarkable properties are extended to multiquadratic extensions of separability degree at most $4$. We also extend to the characteristic $2$ a result of Elman-Lam-Tignol-Wadsworth by constructing an algebra of exponent $2$ and degree $8$ containing a separable triquadratic extension but which admits no adapted decomposition to this extension. As an application we give an elementary proof of the non-excellence of separable biquadratic extensions.
