  We say that the system of equations $Ax=b$, where $A$ is an integer matrix
and $b$ is a (non-zero) integer vector, is partition regular if whenever the
integers are finitely coloured there is a monochromatic vector $x$ with $Ax=b$.
Rado proved that the system $Ax=b$ is partition regular if and only if it has a
constant solution. Byszewski and Krawczyk asked if this remains true when the
integers are replaced by a general ring $R$. Our aim in this note is to answer
this question in the affirmative. The main ingredient is a new `direct' proof
of Rado's result.
