In the study of non-associative algebra, there are at least two different notions of what the half-Bol identity is. Throughout, let L be an algebraic loop and let x, y, and z be elements of L. Some authors use the term half-Bol to refer to the identity ((x y) z) y^α = x((y z) y^α) for α element Z an integer. In this context, there is a strong algebraic duality between algebraic loops L which satisfy the above identity and those which are generalized Bol loops. On the other hand, at least one author use the phrase half-Bol loop to refer to an algebraic loop L for which one can find a mapping τ:L->L such that ((x y) z) y^α = x((y z) y^α).
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