A uniform module is a concept from the field of module theory in algebra, particularly related to the study of Abelian groups and rings. It refers to a type of module that has a certain uniformity property regarding its submodules.
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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 for nonzero , the right ideals , , form an infinite direct sum, contradicting the ascending chain condition.