Extension field as a unital associative algebra

Let $𝐾$ be a field and $𝐿 \leq 𝐾$ be a Subfield. Then $𝐾$ is a commutative K-monoid over $𝐿$ . falg In fact, an extension field $𝐿$ of $𝐾$ is precisely a commutative unital associative division algebra over $𝐾$ .