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For central simple algebras of exponent $2$ over fields of characteristic $2$and $2$-cohomological dimension equal to $2$, we study the adapteddecomposition to some multiquadratic extensions of the base field. Severalremarkable properties are extended to multiquadratic extensions of separabilitydegree at most $4$. We also extend to the characteristic $2$ a result ofElman-Lam-Tignol-Wadsworth by constructing an algebra of exponent $2$ anddegree $8$ containing a separable triquadratic extension but which admits noadapted decomposition to this extension. As an application we give anelementary proof of the non-excellence of separable biquadratic extensions.

Autour de la d\'ecomposition des alg\`ebres d'exposant 2 sur les extensions multiquadratiques