Semilinear action
= Semilinear action
{title2=$\sigma(av)=\sigma(a)\sigma(v)$}
For an extension $L/K$ with <Galois group> $G$, a <semilinear action> on an $L$-space is an additive group action satisfying $\sigma(av)=\sigma(a)\sigma(v)$. Scalar coefficients are transformed along with vectors. Invariants form a $K$-space, and <Galois descent of vector spaces> reconstructs the original space from it.