Function algebra

Let $𝕂$ be a field and $𝑋$ be some set. The function algebra $𝕂 𝑋 = 𝖲 𝖾 𝗍 (𝑋, 𝕂)$ consists of functions $𝑋 \to 𝕂$ with scaling, addition, and multiplication defined pointwise. #m/def/ralg

Additional structure

If $𝑋$ is a topological space, one may consider a Continuous function algebra.
If one restricts to maps of finite support one gets the free module of $X$ over $\mathbb{K}$ .
- In particular, if $𝑋$ is a group this is the group ring.

#state/develop | #lang/en | #SemBr