Normed division algebra
= Normed division algebra
{title2=$D$}
A normed division algebra is a nonzero unital <normed algebra> in which every nonzero element has a two-sided multiplicative inverse. The complex <Gelfand-Mazur theorem> forces such an algebra to be $\mathbb C$, even when completeness is not initially assumed: embed it in its <Banach algebra> completion and use <nonemptiness of the Banach-algebra spectrum>.