[[K-monoid]]
# 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 $L$. #m/thm/falg
In fact, an [[Field extension|extension field]] $L$ of $K$ is precisely a commutative unital associative division algebra over $K$.

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#state/tidy| #lang/en | #SemBr