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.

algebraic loop | Bol loop | generalized Bol loop | Moufang loop

Gerrit Bol