ABSTRACT
Using the concepts of prime module, semiprime module and the concept of ascending chain condition (ACC) on annihilators for an R-module M, we prove that if M is semiprime and projective in σ[M], such that M satisfies ACC on annihilators, then M has finitely many minimal prime submodules. Moreover, if each submodule N⊆M contains a uniform submodule, we prove that there is a bijective correspondence between a complete set of representatives of isomorphism classes of indecomposable non-M-singular injective modules in σ[M] and the set of minimal primes in M. If M is a Goldie module, then , where each Ei is a uniform M-injective module. As an application, new characterizations of left Goldie rings are obtained.
Acknowledgment
The authors want to thank the referee for the carefully reading and the useful comments to improve this paper.