Let $A \in M_{m \times n}(\mathbb{Z})$ be a matrix with integer coefficients. The system of equations $A \vec{x} = \vec{0}$ is said to be partition regular over $\mathbb{Z}$ if for every finite partition $\mathbb{Z} \setminus \{0\} = \cup_{i=1}^r C_i $, there exists a solution $\vec{x}\in \mathbb{Z}^{n}$, all of whose components belonging to the same $C_i$. For example, the equation $x+y-z = 0$ is partition regular. In 1933 Rado characterized completely all partition regular matrices. He also conjectured that for any partition $\mathbb{Z} \setminus \{0\} = \cup_{i=1}^r C_i $, there exists a partition class $C_i$ that contains solutions to all partition regular systems. This conjecture was settled in 1975 by Deuber. We study the analogue of Rado's conjecture in commutative rings, and prove that the same conclusion holds true in any integral domain.