Left Bol magma: Difference between revisions
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A [[magma]] <math>(S,*)</math> is termed a '''left Bol magma''' if it satisfies the following identity for all <math>x,y,z \in S</math>: | A [[magma]] <math>(S,*)</math> is termed a '''left Bol magma''' if it satisfies the following identity for all <math>x,y,z \in S</math>: | ||
<math>\! x | <math>\! x * (y * (x * z)) = (x * (y * x)) * z</math> | ||
Typically, the left Bol identity is studied in the context of [[algebra loop]]s. Such loops are termed [[left Bol loop]]s. However, some of the properties studied for left Bol loops generalize to [[left Bol magma with neutral element|left Bol magmas with neutral element]]. | Typically, the left Bol identity is studied in the context of [[algebra loop]]s. Such loops are termed [[left Bol loop]]s. However, some of the properties studied for left Bol loops generalize to [[left Bol magma with neutral element|left Bol magmas with neutral element]]. | ||
Latest revision as of 16:24, 6 March 2010
This article defines a property that can be evaluated for a magma, and is invariant under isomorphisms of magmas.
View other such properties
Definition
A magma is termed a left Bol magma if it satisfies the following identity for all :
Typically, the left Bol identity is studied in the context of algebra loops. Such loops are termed left Bol loops. However, some of the properties studied for left Bol loops generalize to left Bol magmas with neutral element.