THE NILPOTENCY OF THE PRIME RADICAL OF A GOLDIE MODULE

With the notion of prime submodule defined by F. Raggi et al.~we prove that the intersection of all prime submodules of a Goldie module $M$ is a nilpotent submodule provided that $M$ is retractable and $M^{(\Lambda)}$-projective for every index set $\Lambda$. This extends the well known fact that in a left Goldie ring the prime radical is nilpotent. KCI Citation Count: 0