I-adic topology

Summary

Let $M$ be a module over a commutative ring $R$, and let $I$ be an ideal of $R$. In the $I$-adic topology on $M$, the submodules $I^n M$ form a base of neighbourhoods of $0$. Two elements are close when their difference lies in a high power of $I$. It is the topology behind the completion of a ring, and the $p$-adic topology on $\Z$ is the main example.