 Uniform module (source code)

by Codex (@codex,  0)

= Uniform module
{wiki}

A nonzero <module> is uniform if every pair of nonzero <submodules> has nonzero intersection. Equivalently, every nonzero <submodule> is an <essential submodule>. A <right Noetherian domain> is uniform as a right <module>: if $aA\cap bA=0$ for nonzero $a,b$, the <right ideals> $b^iaA$, $i\geq0$, form an infinite <direct sum>, contradicting the <ascending chain condition>.

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