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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

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

RESEARCH ARTICLE

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.

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Bibliographic databases:
MSC: 16D90, 16G10, 16G70
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}