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http://dx.doi.org/10.5666/KMJ.2011.51.4.375

Baer and Quasi-Baer Modules over Some Classes of Rings  

Haily, Abdelfattah (Departement de Mathematiques et Informatique, Faculte des Sciences)
Rahnaou, Hamid (Departement de Mathematiques et Informatique, Faculte des Sciences)
Publication Information
Kyungpook Mathematical Journal / v.51, no.4, 2011 , pp. 375-384 More about this Journal
Abstract
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.
Keywords
Endomorphism; Idempotent; Annihilator; Baer module; $\mathcal{K}$-nonsingular module;
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