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On Artinian Rings With Restricted Class Of Injectivity Domains

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Date
2013
Author
Aydogdu, Pinar
Sarac, Buelent
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Abstract
In a recent paper of Alahmadi, Alkan and Lopez-Permouth, a ring R is defined to have no (simple) middle class if the injectivity domain of any (simple) R-module is the smallest or largest possible. Er, Lopez-Permouth and Sokmez use this idea of restricting the class of injectivity domains to classify rings, and give a partial characterization of rings with no middle class. In this work, we continue the study of the property of having no (simple) middle class. We give a structural description of right Artinian right nonsingular rings with no right middle class. We also give a characterization of right Artinian rings that are not SI to have no middle class, which gives rise to a full characterization of rings with no middle class. Furthermore, we show that commutative rings with no middle class are those Artinian rings which decompose into a sum of a semisimple ring and a ring of composition length two. Also, Artinian rings with no simple middle class are characterized. We demonstrate our results with several examples. (c) 2012 Elsevier Inc. All rights reserved.
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https://doi.org/10.1016/j.jalgebra.2012.11.027
http://hdl.handle.net/11655/19833
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  • Matematik Bölümü Makale Koleksiyonu [168]
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