Definition:Vector Space on Field Extension

Definition

Let $\struct {K, +, \times}$ be a field.

Let $L / K$ be a field extension over $K$.

Then $\struct {L, +, \times}_K$ is the vector space on $L$ over $K$.

Also see

• Vector Space on Field Extension is Vector Space

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $8$: Field Extensions: $\S 36$. The Degree of a Field Extension