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  "body": "\n## Summary\n\nA uniform module is a nonzero [[module|0NZ8JA25WK]] in which any two nonzero submodules intersect in a nonzero submodule.\nEquivalently, every nonzero submodule is an [[essential submodule|8MS51FASMX]].\nUniform modules are the units for measuring the uniform (Goldie) dimension of a module, which counts how many independent uniform submodules fit inside it.\nThey are a main tool in the proof of Goldie's theorem on rings of quotients of semiprime Noetherian rings.\n\n## Explanations\n\n### L1 human\n\nIn a uniform module, nonzero pieces can never be disjoint: any two of them share a nonzero element.\nSo the module cannot contain two independent directions, as $\\Z \\oplus \\Z$ does.\nThe integers form a uniform $\\Z$-module, since for nonzero $a$ and $b$ the subgroups $a\\Z$ and $b\\Z$ share $ab \\ne 0$.\nEvery uniform module is [[indecomposable|E2P29GCD9T]], since two summands of a direct sum meet only in zero.\n",
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