Corollary

The mapping $\Phi_{L/K}= \Theta \circ \Psi^{-1}$ defines a group isomorphism from Br(L$/K$) to $H^2(G,L^*)$.

Let $K'$ be an extension of K and $\varphi : K'\rightarrow L$ a morphism of K-algebras. The set H of elements $h$ of G such that $\lambda (h)\circ \varphi =\varphi$ is a subgroup of G, and the $K'$-algebra L endowed with the restriction of $\lambda$ to H is a Galois algebra over $K'$.