Simple-Baer rings and minannihilator modules
L Mao - Communications in Algebra, 2012 - Taylor & Francis
L Mao
Communications in Algebra, 2012•Taylor & FrancisLet 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 RR (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 …
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 RR (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 …
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.
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