Corollary 2

For the ring $B$ to be a flat right $A$-module, it is necessary and sufficient that it satisfy the following condition: (RP') Every solution $(y_k)_{1 \leq k \leq n}$, consisting of elements of $B$, of a system of homogeneous linear equations

with coefficients $c_{ki}$ in $A$, is a linear combination with coefficients $b_j \in B$, of solutions $(z_{jk})_{1 \leq k \leq n}$ of the system (15), consisting of elements $z_{jk}$ of $A$.