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A Characterization of Bol left loops

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Abstract

The relationship between the Bol identity, the so-called Left Loop Property LLP and the Left Inverse Property in any left quasigroup is determined. Counterexamples are given whenever two properties are not equivalent. It is shown that a principal isotope of a LLP quasigroup is a left Bol loop. In any LLP left quasigroup the existence of a right identity element is equivalent to the right division.

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Authors and Affiliations

  1. D’epartement de Mathématiques, iversité d’Abomey-Calavi 01 B.P., 4521, Cotonou 01, Bénin

    A. Nourou Issa

  2. Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, 20146, Hamburg

    Alexander Kreuzer

Authors
  1. A. Nourou Issa
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  2. Alexander Kreuzer
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Correspondence to A. Nourou Issa.

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Dedicated to Prof. Dr. Dr. h.c. Herbert Zeitler on the occasion of his 80th birthday

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Nourou Issa, A., Kreuzer, A. A Characterization of Bol left loops. Results. Math. 44, 106–113 (2003). https://doi.org/10.1007/BF03322917

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