Algebraic structure of $\{0,1,\ldots,+\infty\}$

Question

I am reading about the dimension of a commutative ring $A$ with identity $1\ne0$, which is defined as the supremum of the heights of its prime ideals. I think it turns out that the dimension is always well-defined to be in $\{0,1,\ldots,+\infty\}$. My question is, is there some algebraic structure on $\{0,1,\ldots,+\infty\}$? There is an addition $+$ and a relation $\le$, and certain properties are satisfied. Is there some named algebraic structure which this is an example of?

Answer 1

It's an abelian ordered monoid.