V-ring (ring theory)

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