Unitization

Summary

The unitization of an algebra $A$ is the algebra $\mathbb{K} \oplus A$ with a product that makes $(1, 0)$ a unit. It contains $A$ as an ideal of codimension one. It lets one apply tools that need a unit, such as invertibility and the spectrum, to algebras without one. For normed algebras and Banach algebras it carries a natural norm, and for C*-algebras a natural C*-norm.