What is the meaning of $K/F$ is a cyclic extension?

Question

I have it that $K/F$ is a (finite) field extension, what is the definition of when $K/F$ is called cyclic ?

I heard it while I studied Galois theory and it was defined as

$K/F$ is called cyclic if $Gal(K/F)$ is a cyclic group

where the notation $Gal$ means that $K/F$ is also Galois.

Does, in general, it means $Aut(K/F)$ is cyclic, without the requirement that the extension is Galois ? (how it is defined in the literature/what is the convention ?)

Answer 1

An extension of fields $K/L$ is called Galois if its both separable and normal. An extension is called abelian if $K/L$ is Galois and the Galois group $\mathrm{Gal}(K/L)$ is abelian and cyclic if the Galois group is cyclic.