Abstract
It is well-known that if R is a left Noetherian ring, then there is a bijective correspondence between minimal prime ideals of R and maximal torsion radicals of R-Mod. Using the notion of a prime M-ideal, it is shown that this correspondence can be extended to the category σ[M] of modules subgenerated by a module M, provided that M is a Noetherian quasi-projective generator in σ[M]. Furthermore, under this hypothesis the prime M-ideals are the fully invariant submodules P of M such that M/P is semi-compressible.
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