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A note on topological divisors of zero and division algebras

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Abstract

We prove that normed unital complex (possibly non-associative) algebras with no non-zero left topological divisor of zero are isomorphic to the field \(\mathbb {C} \) of complex numbers. We also show the existence of a complete normed unital infinite-dimensional complex algebra with no non-zero two-sided topological divisor of zero.

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Acknowledgments

We would like to express our gratitude to M. Cabrera and A. Kaidi for helpful comments and suggestions concerning the topic of this paper. We also thank the referees for their suggestions to improve the presentation of the paper.

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Authors and Affiliations

  1. I.E.S. Generalife, Calle Huerta del Rasillo 1, 18004 , Granada, Spain

    J. Carlos Marcos

  2. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 , Granada, Spain

    Ángel Rodríguez-Palacios & M. Victoria Velasco

Authors
  1. J. Carlos Marcos
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  2. Ángel Rodríguez-Palacios
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  3. M. Victoria Velasco
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Corresponding author

Correspondence to M. Victoria Velasco.

Additional information

Partially supported by Junta de Andalucía grants FQM 0199 and FQM 3737, and Project MTM-2009-12067.

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Marcos, J.C., Rodríguez-Palacios, Á. & Velasco, M.V. A note on topological divisors of zero and division algebras. RACSAM 109, 93–100 (2015). https://doi.org/10.1007/s13398-014-0168-4

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  • DOI: https://doi.org/10.1007/s13398-014-0168-4

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