The Galois extension of semi-local rings

How to get a Galois extension of the commutative semi-local ring $R=\mathbb{F}_2+v\mathbb{F}_2$, where $v^2=v$. The Galois extension of $R$ of degree $d$ is $\mathbb{F}_a+v\mathbb{F}_a$ where $a=2^d$ or not?

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