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Simple rings with injectivity conditions on one-sided ideals

Published online by Cambridge University Press:  17 April 2009

John Clark  and
Dinh Van Huynh
John Clark
Affiliation:
Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin, New Zealand e-mail: jclark@maths.otago.ac.nz
Dinh Van Huynh
Affiliation:
Department of Mathematics, Ohio University, Athens, OH. 45701, United States of America e-mail: huynh@math.ohiou.edu
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This paper looks at simple rings which have right ideals satisfying various types of injectivity conditions. We characterise when a simple regular ring is right self-injective and show that if R is a simple ring in which every right ideal is the direct sum of quasi-continuous right ideals then R is either Artinian or a non-selfinjective right Goldie ring in which every right ideal is a direct sum of uniform right ideals.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 2 , October 2007 , pp. 315 - 320
Copyright
Copyright © Australian Mathematical Society 2007

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