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Left, right, and inner socles of associative systems

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Abstract

We investigate the basic properties of the different socles that can be considered in not necessarily semiprime associative systems. Among other things, we show that the socle defined as the sum of minimal (or minimal and trivial) inner ideals is always an ideal. When trivial inner ideals are included, this inner socle contains the socles defined in terms of minimal left or right ideals.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Oviedo, C/ Calvo Sotelo S/N, 33007, Oviedo, Spain

    José A. Anquela & Teresa Cortés

  2. Departamento de Álgebra, Geometría, y Topología, Facultad de Ciencias, Universidad de Málaga, Campus De Teatinos, 29071, Málaga, Spain

    Miguel Gómez-Lozano & Mercedes Siles-Molina

Authors
  1. José A. Anquela
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  2. Teresa Cortés
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  3. Miguel Gómez-Lozano
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  4. Mercedes Siles-Molina
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Anquela, J.A., Cortés, T., Gómez-Lozano, M. et al. Left, right, and inner socles of associative systems. Acta Mathematica Hungarica 103, 177–196 (2004). https://doi.org/10.1023/B:AMHU.0000028407.60750.64

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  • DOI: https://doi.org/10.1023/B:AMHU.0000028407.60750.64

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