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