2016/01/13 by Jaime Castro Pérez, Mauricio Medina-Bárcenas, Mauricio Medina Bárcenas +8
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Rings, Modules, and Algebras #math.RA #msc:16D50 #msc:16D80 #msc:16P50 #msc:16P70
paper · pdf · doi:10.48550/arxiv.1601.03436
arxiv created 2016/01/13 · arxiv updated 2016/01/15
For an R-module M, projective in σ[M] and satisfying ascending chain condition (ACC) on left annihilators, we introduce the concept of Goldie module. We also use the concept of semiprime module defined by Raggi et. al. in \citeS 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, we 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.