Baer and Quasi-Baer Modules over Some Classes of Rings

  • Haily, Abdelfattah ;
  • Rahnaou, Hamid
  • Received : 2011.01.27
  • Accepted : 2011.08.21
  • Published : 2011.11.23


We study Baer and quasi-Baer modules over some classes of rings. We also introduce a new class of modules called AI-modules, in which the kernel of every nonzero endomorphism is contained in a proper direct summand. The main results obtained here are: (1) A module is Baer iff it is an AI-module and has SSIP. (2) For a perfect ring R, the direct sum of Baer modules is Baer iff R is primary decomposable. (3) Every injective R-module is quasi-Baer iff R is a QI-ring.


Endomorphism;Idempotent;Annihilator;Baer module;$\mathcal{K}$-nonsingular module


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