K-monoid

Division algebra

A division algebra (𝐴, ⋅) is at once a K-monoid and a division ring, falg hence for every nonzero 𝑎 ∈𝐴 there exists some (necessarily unique) 𝑎−1 ∈𝐴 such that 𝑎−1𝑎 =𝑎𝑎−1 =1𝐴.

Properties

• Division algebra with only algebraic elements over an algebraically closed field

---

tidy | en | SemBr