Past exam of the options I course of the University of Oxford / 2006 / B / B1 / i

A field extension $K/F$ is finite when $K$, regarded as a vector space over $F$, has finite dimension. Its degree of a field extension isThus a finite basis $u_1,\dots ,u_m$ means that every $k\in K$ is uniquely expressible as ${\sum }_i{c}_i{u}_i$ with coefficients $c_i\in F$.