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ABSTRACT
In this note, we study the notion of purely infinite simple ring in the case of nonunital rings, and we obtain an analog to Zhang's Dichotomy for σ-unital purely infinite simple C*-algebras in the purely algebraic context.
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ACKNOWLEDGMENTS
We thank P. Ara for valuable discussions during the preparation of this note.
The first author was supported by an FPU fellowship of the Junta de Andalucía. Both authors are partially supported by the DGI and European Regional Development Fund, jointly, through Project MTM2004-00149, and by PAI III grant FQM-298 of the Junta de Andalucía. Also, the second author is partially supported by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya.
Notes
Communicated by A. Facchini.