The decoupling problem by static-state feedback for a system with coef
ficients in a ring is investigated using a geometric approach. The not
ion of a precontrollability submodule, which captures the geometric as
pects of the notion of controllability subset of the state space in th
e present context, is introduced and it is used for stating solvabilit
y conditions for the decoupling problem for a system with coefficients
in a Noetherian ring. This result extends and improves previous resul
ts concerning systems with coefficients in a principal ideal domain an
d it fan, in particular, be used for dealing with decoupling problem i
nvolving delay-differential systems.