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).
