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Purely Baer Modules | ||
| Al-Mustansiriyah Journal of Science | ||
| Article 1, Volume 24, Issue 5, 2013, Pages 187-198 | ||
| Author | ||
| Mehdi S. Abbas | ||
| Abstract | ||
| In this work, we introduced the notion of purely Baer property of modules as a generalization to that of Baer property. This notion depends on studying the relation between the modules and their endomorphism rings through the purity of annihilators. We show that direct summands inherit this property and that, every finitely generated abelian group is purely Baer if and only if it is semi-simple or torsionfree. We provided examples to show that direct sums of purely Baer modules are not so. But arbitrary direct sum of matually subisomorphic purely Baer modules is purely Baer, and that every free module over purely Baer ring is purely Baer. We give number of characterizations and properties of purely Baer modules and extend some useful results of Baer rings to the general module theoretic setting. (2010) Mathematics Subject Classification: 16D10 , 16D50 | ||
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