Field extension

Remarks

Often one also calls $L$ an extension of $K$ when there is an injective ring homomorphism $K \to L$. Then one identifies $K$ with its image. An extension $L/K$ makes $L$ a vector space over $K$. Its dimension is the degree of the extension. Examples: $\mathbb{C}/\mathbb{R}$, $\mathbb{R}/\mathbb{Q}$ and $\mathbb{Q}(\sqrt{2})/\mathbb{Q}$. The notation $L/K$ does not mean a quotient.