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A note on Baer and Quasi-Baer modules | ||
| Al-Mustansiriyah Journal of Science | ||
| Article 1, Volume 21, Issue 5, 2010, Pages 450-461 | ||
| Author | ||
| Mehdi S. Abbas | ||
| Abstract | ||
| We give new characterizations of Baer and quasi-Baer modules. We study the direct sums of (quasi-)Baer modules and we give a sufficient condition under which the direct sums of (quasi-)Baer modules has the (quasi-)Baer property. Also we extended some results from the rings theory to the modules theory. We study the endomorphism ring of Baer and quasi-Baer modules and we show that : If M is a quasi-injective R-module . Then M is Baer iff S = EndR(M) is Von Neumann regular ring. Also we show that if M is an R-module whose endomorphism ring S = EndR(M) is extending, then M is Baer iff S is right nonsingular ring. As another we show that if M is an R-module such that S = EndR(M) has no infinite set of non-zero orthogonal idempotents. Then M is Baer iff S is right Rickart ring | ||
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