Simple-Baer Rings and Minannihilator Modules

Let R be a ring. M is said to be a minannihilator left R-module if r M l R (I) = IM for any simple right ideal I of R. A right R-module N is called simple-flat if Nl R (I) = l N (I) for any simple right ideal I of R. R is said to be a left simple-Baer (resp., left simple-coherent) ring if the left annihilator of every simple right ideal is a direct summand of R R (resp., finitely generated). We first obtain some properties of minannihilator and simple-flat modules. Then we characterize simple-coherent rings, simple-Baer rings, and universally mininjective rings using minannihilator and simple-flat modules.