Geodesic
On radical square zero rings
Algebra and discrete mathematics, Tome 14 (2012) no. 2, pp. 297-306.

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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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Claus Michael Ringel; B.-L. Xiong. On radical square zero rings. Algebra and discrete mathematics, Tome 14 (2012) no. 2, pp. 297-306. http://geodesic.mathdoc.fr/item/ADM_2012_14_2_a11/

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