Terminology: definition of closed submodule

Question

I am unable to find any clear definition of the concept of a closed submodule of a module. I'd really appreciate it if someone might elaborate on it, or point me in the right direction.

As far as I can tell, it seems to be an abstraction of the concept of a closed subspace of a vector space. This makes me think that in the case of finite-generation, any submodule is necessarily a closed submodule. Is this correct?

Thanks as always,

M

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Questions: Suppose $R$ is a ring with some ideal $I$. Let $M$ be an $R$-module.

1. What is meant by a closed submodule of $M$?
2. Is $IM$ a closed submodule of $M$?
3. Does this coincide with the notion of being "closed" in the induced topology on $M$ if $R$ is a topological ring?

I am in particular dealing with finitely-generated modules.