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Algebra and Discrete Mathematics, 2012, Volume 14, Issue 2, Pages 297–306
(Mi adm100)
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This article is cited in 5 scientific papers (total in 5 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.
Received: 24.05.2012 Revised: 17.01.2013
Citation:
Claus Michael Ringel, B.-L. Xiong, “On radical square zero rings”, Algebra Discrete Math., 14:2 (2012), 297–306
Linking options:
https://www.mathnet.ru/eng/adm100 https://www.mathnet.ru/eng/adm/v14/i2/p297
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