I'm having a hard time understanding fields. Could someone help with the following
I need to show that if $F$ $\subseteq$ $K$ are both fields and addition and multiplication on F are the restrictions of addition and multiplication on $K$($F$ is a subfield of $K$) then $K$ can be thought of as an $F$-vector space with addition just the addition on $K$ and scalar multiplication by elements of $F$ simply multiplication by elements of $F$.
What does it mean when by 'F-vector space'?
Would I have to check all the fields axioms?
Vector space is an abelian group first: that is the group of vectors. But that is not enough. We also need to have a concept of scalar multiplication. These scalars are 'aliens': they are from another object, a field. ANd there are various conditions the alien field's addition and multiplication has to satisfy to interact 'compatibly' with the addition operation of vectors.
The vectos space is called $F$-vector space if that alien field is F.