Modules whose quotients have finite Goldie dimension

Abstract

If M is a module and M is a submodule of M, then N is irreducible in M if N cannot be written as a proper intersection of two submodules of M. The purpose of this note is to study modules whose submodules can be written as a finite intersection of irreducible submodules. Such modules are characterized by the fact that their quotients all have finite Goldie dimension, so they are called q.f.d. modules.