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:
  1. Every simple left R-module is injective
  2. The radical of every left R-module is zero
  3. 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.