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...
Guardado en:
Autores principales: | , , |
---|---|
Lenguaje: | English |
Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2021
|
Materias: | |
Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172021000100085 |
Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
Sumario: | 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. |
---|