This article is cited in 5 papers

RESEARCH ARTICLE

On radical square zero rings

Claus Michael Ringel^ab, B.-L. Xiong<sup>c

a</sup> 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.

MSC: 16D90, 16G10, 16G70

Received: 24.05.2012
Revised: 17.01.2013

Language: English

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