We say that a ring with identity $R$ is stably finite if for every $n \in \mathbb{N}$, for $A$ and $B$, $n \times n$ matrices with coefficients in $R$ such that $AB = I_n$ necessarily, $BA = I_n$.
Anyone knows a reference that shows that this condition implies the Invariant Basis Number property for the ring $R$, that is, if $R^n \simeq R^m$ as $R$-modules hence $n = m$.
Thanks.
