On Artinian rings with restricted class of injectivity domains.
From MaRDI portal
Publication:371390
DOI10.1016/J.JALGEBRA.2012.11.027zbMATH Open1292.16003arXiv1211.5763OpenAlexW2072065245WikidataQ123138720 ScholiaQ123138720MaRDI QIDQ371390
Author name not available (Why is that?)
Publication date: 9 October 2013
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1211.5763
No records found.
No records found.
This page was built for publication: On Artinian rings with restricted class of injectivity domains.
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q371390)
