In this paper, we study the relationship between the ideal submodules and the topologically complementable submodules of a Hilbert C∗-module. We derive new characterizations and properties for ideal submodules and apply them to provide the conditions under which the topologically complementable submodules are ideal submodules or ideal submodules are topologically complementable submodules. Especially, we show that an ideal submodule in a full Hilbert C∗-module is topologically complementable if and only if it is orthogonally complementable and in this case the orthogonal complement is the unique topological complement for it.
