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In mathematics, a V-ring is a ring R such that every simple R-module is injective. The following three conditions are equivalent: 1. * Every simple left (resp. right) R-module is injective 2. * The radical of every left (resp. right) R-module is zero 3. * Every left (resp. right) ideal of R is an intersection of maximal left (resp. right) ideals of R A commutative ring is a V-ring if and only if it is Von Neumann regular.
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