Baer and Quasi-Baer Modules over Some Classes of Rings

• Journal title : Kyungpook mathematical journal
• Volume 51, Issue 4,  2011, pp.375-384
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2011.51.4.375
Title & Authors
Baer and Quasi-Baer Modules over Some Classes of Rings
Haily, Abdelfattah; Rahnaou, Hamid;

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;$\small{\mathcal{K}}$-nonsingular module;
Language
English
Cited by
1.
On weak Rickart modules, Journal of Algebra and Its Applications, 2017, 16, 09, 1750165
2.
Direct sums of quasi-Baer modules, Journal of Algebra, 2016, 456, 76
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