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Algebra Discrete Math., 2012, Volume 14, Issue 2, Pages 297–306 (Mi adm100)  

This article is cited in 2 scientific papers (total in 2 papers)

RESEARCH ARTICLE

On radical square zero rings

Claus Michael Ringelab, B.-L. Xiongc

a Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
b King Abdulaziz University, P O Box 80200, Jeddah, Saudi Arabia
c Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, P. R. China

Abstract: Let $\Lambda$ be a connected left artinian ring with radical square zero and with $n$ simple modules. If $\Lambda$ is not self-injective, then we show that any module $M$ with $\operatorname{Ext}^i(M,\Lambda)=0$ for $1 \le i \le n+1$ is projective. We also determine the structure of the artin algebras with radical square zero and $n$ simple modules which have a non-projective module $M$ such that $\operatorname{Ext}^i(M,\Lambda) = 0$ for $1 \le i \le n$.

Keywords: Artin algebras; left artinian rings; representations, modules; Gorenstein modules, CM modules; self-injective algebras; radical square zero algebras.

Full text: PDF file (174 kB)
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Bibliographic databases:
MSC: 16D90, 16G10, 16G70
Received: 24.05.2012
Revised: 17.01.2013
Language:

Citation: Claus Michael Ringel, B.-L. Xiong, “On radical square zero rings”, Algebra Discrete Math., 14:2 (2012), 297–306

Citation in format AMSBIB
\Bibitem{RinXio12}
\by Claus~Michael~Ringel, B.-L.~Xiong
\paper On radical square zero rings
\jour Algebra Discrete Math.
\yr 2012
\vol 14
\issue 2
\pages 297--306
\mathnet{http://mi.mathnet.ru/adm100}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3099976}
\zmath{https://zbmath.org/?q=an:1288.16013}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Chen X.-W., Ye Yu., “Retractions and Gorenstein Homological Properties”, Algebr. Represent. Theory, 17:3 (2014), 713–733  crossref  mathscinet  zmath  isi  scopus
    2. C. M. Ringel, P. Zhang, “Representations of quivers over the algebra of dual numbers”, J. Algebra, 475 (2017), 327–360  crossref  mathscinet  zmath  isi  scopus
  • Algebra and Discrete Mathematics
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