At page $105$ of Introduction to Commutative Algebra of M. Atiyah, there is the following claim:
C. Given a ring $A$ and an ideal $I\subset A$, consider the filtration $(I^n)_{n\in\mathbb{N}}$, then we have a the $I$-adic topology on $A$. Then $A$ with this topology is a topological ring.
I'm able to check that $A$ is a topological group, but I have some problems to check that the multiplication map $A\times A\longrightarrow A$ is continuos.
Can anyone help me?