In the study of non-associative algebra, there are at least two different notions of what the half-Bol identity is. Throughout, let be an algebraic loop and let , , and be elements of .
Some authors use the term half-Bol to refer to the identity
for an integer. In this context, there is a strong algebraic duality between algebraic loops which satisfy the above identity and those which are generalized Bol loops (Adeniran and Solarin 1999).
On the other hand, at least one author use the phrase half-Bol loop to refer to an algebraic loop for which one can find a mapping such that
In this context, there is a considerable amount of variability as the mapping may or may not be assumed nonzero and may also be assumed to satisfy various other conditions as well (Boerner and Kallaher 1982).