Example of $I$-adic topology of submodule not matching subspace topology? I'm reading about the $I$-adic topology on $M$ for $R$ a commutative ring, $I$ an ideal of $R$ and $M$ an $R$-module. The references I'm reading don't provide examples, but they say that if $N$ is a submodule of $M$, it's not necessarily true that the subspace topology of $N$ in $M$ with the $I$-adic topology coincides with the $I$-adic topology on $M$ (of course, I know this holds for $R$ Noetherian and $M$ a finite $R$-module by Artin-Rees).

Does anyone know of any specific examples where these topologies don't coincide? Thank you very much!
Look this for instance: https://mathoverflow.net/questions/71699/counter-examples-to-krulls-intersection-theorem if it may help.
Look this for instance: https://mathoverflow.net/questions/71699/counter-examples-to-krulls-intersection-theorem if it may help.