Suppose we define topological a ring $A$ with $I$-adic topology. Then we can talk about neighbourhood {$x+I^n|$for some $n>0$, and $x\in A$} in $A$. But I don't know how to describe the structre of discrete topology on a ring?
In analysis, we can use metrics to define discrete topology, but in general algebra, we don't have such tools. I guess we can make the discrete topology by requiring $I^2=(0)$. Hope someone could help. Thanks!
We can make the discrete topology by requiring $I=(0)$.