2016/01/13 by Jaime Castro Pérez, Pérez, Jaime Castro, Mauricio Medina-Bárcenas +5
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Rings, Modules, and Algebras #math.RA #msc:16D50 #msc:16P50 #msc:16P70 #msc:16S90
paper · pdf · doi:10.48550/arxiv.1601.03438
arxiv created 2016/01/13 · arxiv updated 2016/01/15
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 Goldie module then % M≅ E1^k1⊕ E2^k2⊕ ...⊕ En^kn where each Ei is a uniform M-injective module. As an application, new characterizations of left Goldie rings are obtained.