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dc.contributor.authorAydogdu, Pinar
dc.contributor.authorSarac, Buelent
dc.date.accessioned2019-12-16T09:40:17Z
dc.date.available2019-12-16T09:40:17Z
dc.date.issued2013
dc.identifier.issn0021-8693
dc.identifier.urihttps://doi.org/10.1016/j.jalgebra.2012.11.027
dc.identifier.urihttp://hdl.handle.net/11655/19833
dc.description.abstractIn 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.
dc.language.isoen
dc.publisherAcademic Press Inc Elsevier Science
dc.relation.isversionof10.1016/j.jalgebra.2012.11.027
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectMathematics
dc.titleOn Artinian Rings With Restricted Class Of Injectivity Domains
dc.typeinfo:eu-repo/semantics/article
dc.relation.journalJournal Of Algebra
dc.contributor.departmentMatematik
dc.identifier.volume377
dc.identifier.startpage49
dc.identifier.endpage65
dc.indexingWoS
dc.indexingScopus


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