Modules with ascending chain condition on annihilators and Goldie modules Academic Article in Scopus uri icon

abstract

  • © 2017, Copyright © Taylor & Francis.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 ¿[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 ¿[M] and the set of minimal primes in M. If M is a Goldie module, then (Formula presented.), where each Ei is a uniform M-injective module. As an application, new characterizations of left Goldie rings are obtained.

publication date

  • June 3, 2017