New algebraic properties of middle Bol loops II

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 meth...

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Autores principales:	Jaiyéolá,T. G., David,S. P., Oyebola,O. O.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2021
Materias:	Bol loops Middle Bol loops Moufang loops
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000100085
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spelling	oai:scielo:S0716-091720210001000852021-01-26New algebraic properties of middle Bol loops IIJaiyéolá,T. G.David,S. P.Oyebola,O. O. 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.40 n.1 20212021-02-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000100085en10.22199/issn.0717-6279-2021-01-0006
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Bol loops Middle Bol loops Moufang loops
spellingShingle	Bol loops Middle Bol loops Moufang loops Jaiyéolá,T. G. David,S. P. Oyebola,O. O. New algebraic properties of middle Bol loops II
description	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	Jaiyéolá,T. G. David,S. P. Oyebola,O. O.
author_facet	Jaiyéolá,T. G. David,S. P. Oyebola,O. O.
author_sort	Jaiyéolá,T. G.
title	New algebraic properties of middle Bol loops II
title_short	New algebraic properties of middle Bol loops II
title_full	New algebraic properties of middle Bol loops II
title_fullStr	New algebraic properties of middle Bol loops II
title_full_unstemmed	New algebraic properties of middle Bol loops II
title_sort	new algebraic properties of middle bol loops ii
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2021
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000100085
work_keys_str_mv	AT jaiyeolatg newalgebraicpropertiesofmiddlebolloopsii AT davidsp newalgebraicpropertiesofmiddlebolloopsii AT oyebolaoo newalgebraicpropertiesofmiddlebolloopsii
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New algebraic properties of middle Bol loops II

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