As per the definition of field :
Field F is a non empty set with 2 binary operations called 'addition'(+) and 'multiplication'(.).For F to be a field it must satisfy the following conditions:
1.(F,+) is an abelian group
2.(F-{0},.) is a group
3. Multiplication is distributed over addition
Vector Space:A non empty set V is said to be a vector space over field F if it satisfies the following conditions:
1.(V,+) is an abelian group
2.if c belongs to F,cv belongs to V, v belongs to V.
Scalar multiplication satisfies the following conditions:
1.(c1+c2)v=c1v+c2v c1,c2 belongs to F and v belongs to V
2.c(v1+v2)=cv1+cv2 c belongs to F v1,v2 belong to V
3.c1(c2v)=(c1c2)v
4.1v=v
i.e 1 is multilicative identity of F.
So does this mean that multiplication of F is conventional multiplication.If that is the case then (f-{0},.) is an abelian group.
That would mean no vector space can be defined over some fields.
However I also know Field is a vector space over itself.
Please clarify my doubt