Uniform module

Summary

A uniform module is a nonzero module in which any two nonzero submodules intersect in a nonzero submodule. Equivalently, every nonzero submodule is an essential submodule. Uniform modules are the units for measuring the uniform (Goldie) dimension of a module, which counts how many independent uniform submodules fit inside it. They are a main tool in the proof of Goldie's theorem on rings of quotients of semiprime Noetherian rings.