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New algebraic properties of middle Bol loops II

  • Jaiyeola, Temitope Gbolahan [1] ; David, S. P. [1] ; Oyebola, O. O.
    1. [1] Obafemi Awolowo University

      Obafemi Awolowo University

      Nigeria

  • Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 1, 2021, págs. 85-106
  • Idioma: inglés
  • DOI: 10.22199/issn.0717-6279-2021-01-0006
  • Enlaces
  • Resumen
    • A loop (Q, ·, \, /) is called a middle Bol loop (MBL) if it obeys the identity x(yz\x)=(x/z)(y\x). To every MBL corresponds a right Bol loop (RBL) and a left Bol loop (LBL). In this paper, some new algebraic properties of a middle Bol loop are established in a different style. Some new methods of constructing a MBL by using a non-abelian group, the holomorph of a right Bol loop and a ring are described. Some equivalent necessary and sufficient conditions for a right (left) Bol loop to be a middle Bol loop are established. A RBL (MBL, LBL, MBL) is shown to be a MBL (RBL, MBL, LBL) if and only if it is a Moufang loop.

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