[[K-monoid]]
# Division algebra

A **division algebra** $(A, \cdot)$ is at once a [[K-monoid]] and a [[division ring]], #m/def/falg 
hence for every nonzero $a \in A$ there exists some (necessarily unique) $a^{-1} \in A$ such that $a^{-1}a = aa^{-1} = 1_{A}$.

## Properties

- [[Division algebra with only algebraic elements over an algebraically closed field]]

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