Do matrices over noncommutative division rings have well-defined ranks?

Question

It is known that the row and column rank of any matrix over a field are the same and their common value is simply called the rank of the matrix.

Now, for any $m$-by-$n$ matrix $A$ with entries in a noncommutative division ring $D$, one could consider the following four ranks:

1. The dimension of the left $D$-submodule of $D^m$ generated by the columns of $A$.
2. The dimension of the right $D$-submodule of $D^m$ generated by the columns of $A$.
3. The dimension of the left $D$-submodule of $D^n$ generated by the rows of $A$.
4. The dimension of the right $D$-submodule of $D^n$ generated by the rows of $A$.

Are the above four ranks then always the same? If not, then there should be a counterexample for $D$ the Hamiltonian quaternions.