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Converse of "generalized Hilbert 90" / Galois descent

Let $R$ be a finite dimensional $L$-algebra with an action of ${\rm Gal}(L/K)$ such that $\sigma (\lambda .r)=\sigma (\lambda )\sigma (r)$, $\lambda\in L$, $r\in R$, $\sigma\in {\rm Gal}(L/K)$. Then ...
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