Artinian ring
A module "M" is said to have the "double centralizer property" or to be a "balanced module" if C"E"(C"E"("R""M")) = "R""M", where "E" = End("M") and "R""M" are as given in the motivation section. In this terminology, the Artinian ring version of the double centralizer theorem states that simple right modules for right Artinian rings are balanced modules.