New algebraic properties of middle Bol loops II
Author
Jaiyeola, Temitope Gbolahan
David, S. P.
Oyebola, O. O.
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/369410.22199/issn.0717-6279-2021-01-0006
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.