New algebraic properties of middle Bol loops II

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2021-01-0006

Keywords:

Bol loops, Middle Bol loops, Moufang loops

Abstract

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.

Author Biographies

Temitope Gbolahan Jaiyeola, Obafemi Awolowo University.

Dept. of Mathematics.

S. P. David, Obafemi Awolowo University.

Dept. of Mathematics.

O. O. Oyebola, Federal University of Agriculture.

Dept. of Mathematics.

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Published

2021-01-06

How to Cite

[1]
T. G. Jaiyeola, S. P. David, and O. O. . Oyebola, “New algebraic properties of middle Bol loops II”, Proyecciones (Antofagasta, On line), vol. 40, no. 1, pp. 85-106, Jan. 2021.

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