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Communications in Algebra Volume 33, 2005 - Issue 7
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Original Articles

Generalized Quasi-Baer Rings

A. Moussavi Department of Mathematics, University of Tarbiat Modarres, Tehran, IranCorrespondence[email protected]
,
H. Haj Seyyed Javadi Department of Mathematics, Arak University, Arak, Iran
&
E. Hashemi Department of Mathematics, Shahrood University ofTechnology, Shahrood, Iran
Pages 2115-2129 | Received 15 Nov 2003, Published online: 03 Sep 2006
 
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ABSTRACT

We say a ring with identity is a generalized right (principally) quasi-Baer if for any (principal) right ideal I of R, the right annihilator of In is generated by an idempotent for some positive integer n, depending on I. The behavior of the generalized right (principally) quasi-Baer condition is investigated with respect to various constructions and extensions. The class of generalized right (principally) quasi-Baer rings includes the right (principally) quasi-Baer rings and is closed under direct product and also under some kinds of upper triangular matrix rings. The generalized right (principally) quasi-Baer condition is a Morita invariant property. Examples to illustrate and delimit the theory are provided.

Mathematics Subject Classification:

ACKNOWLEDGMENT

The authors are deeply indebted to Professor Gary F. Birkenmeier and the referee for many helpful comments and suggestions for the improvement of this paper.

Notes

#Communicated by M. Ferrero.

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