# Ring theory

They are just functions $f:\mathbb R^n\to\mathbb R$. When $n=1$, $f$ is a real-valued function of a single real variable.
The set of all functions $f:\mathbb R^n\to\mathbb R$ forms an integral domain with addition and multiplication defined as follows: for all $\mathbf x\in\mathbb R^n$, $(f+g)(\mathbf x)\equiv f(\mathbf x)+g(\mathbf x)$ and $(fg)(\mathbf x)\equiv f(\mathbf x)g(\mathbf x)$.