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:

Every simple left R-module is injective.
The radical of every left R-module is zero.
Every left ideal of R is an intersection of maximal left ideals of R.

A commutative ring is a V-ring if and only if it is Von Neumann regular.