On Semiprime Goldie Modules

Abstract

For an R-module M, projective in σ[M] and satisfying ascending chain condition on left annihilators, the authors introduce the concept of Goldie module. The authors also use the concept of semiprime module defined by Raggi et al. in [15] to give necessary and sufficient conditions for an R-module M, to be a semiprime Goldie module. This theorem is a generalization of Goldie's theorem for semiprime left Goldie rings. Moreover, the authors prove that M is a semiprime (prime) Goldie module if and only if the ring S = EndR(M) is a semiprime (prime) right Goldie ring. Also, we study the case when M is a duo module.