TITLE: Examples of non-abstract rings?
QUESTION [6 upvotes]: In group theory, it helped me a lot to use symmetry groups of geometrical objects like a triangle to understand the more abstract concepts. Are there rings with a similar low level of abstractness?
I know $\mathbb{Z}$, $\mathbb{Z}[X]$, $K[X]$ and $\mathbb{Z}[\sqrt{d}], d \in \mathbb{Z}$ which are all quite abstract. Maybe not $\mathbb{Z}$ but it is too "nice" and doesn't illustrate the more interesting properties of rings or the lack thereof very well.

REPLY [3 votes]: The set of continuous functions $\mathcal{C}(\mathbb{R})$ from $\mathbb{R} $ to $\mathbb{R}$ is a ring under addition and multiplication defined as follows: $(f*g) (x) = f(x)g(x)$ and $(f+g)(x)=f(x)+g(x)$, this ring is also an interesting zoo of many interesting ring theoretic activities.