 Underlying field of a vector space

Every vector space is defined over a field.

E.g. in ${\mathbb{R}}^3$, the underlying field is $\mathbb{R}$, the real numbers. And in ${\mathbb{C}}^2$ the underlying field is $\mathbb{C}$, the complex numbers.

Any field can be used, including finite field. But the underlying thing has to be a field, because the definitions of a vector need all field properties to hold to make sense.

Elements of the underlying field of a vector space are known as scalar.