On Maximal Torsion Radicals, IV

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.

Key Words:

• Maximal torsion radical
• Prime M-ideal
• Quasi-projective
• Semi-compressible

2010 Mathematics Subject Classification:

• 16S90
• 16P40
• 16D50