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Quasi-Baer ring extensions and biregrular rings

Published online by Cambridge University Press:  17 April 2009

Gary F. Birkenmeier ,
Jin Yong Kim  and
Jae Keol Park
Gary F. Birkenmeier
Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette LA 70504–1010, United States of America, e-mail: gfb1127@usl.edu
Jin Yong Kim
Affiliation:
Department of Mathematics, Busan National University, Busan 609–735, South Korea, e-mail: jkpark@hyowon.cc.pusan.ac.kr
Jae Keol Park
Affiliation:
Department of Mathematics, Kyung Hee University, Suwon 449–701, South Korea, e-mail: jykim@nms.kyunghee.ac.kr
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Abstract

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A ring R with unity is called a (quasi-) Baer ring if the left annihilator of every (left ideal) nonempty subset of R is generated (as a left ideal) by an idempotent. Armendariz has shown that if R is a reduced PI-ring whose centre is Baer, then R is Baer. We generalise his result by considering the broader question: when does the (quasi-) Baer condition extend to a ring from a subring? Also it is well known that a regular ring is Baer if and only if its lattice of principal right ideals is complete. Analogously, we prove that a biregular ring is quasi-Baer if and only if its lattice of principal ideals is complete.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 1 , February 2000 , pp. 39 - 52
Copyright
Copyright © Australian Mathematical Society 2000

References

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