The half-Bol identity has at least two different meanings in non-associative algebra. Throughout, let 
be an algebraic loop and let 
, 
, and 
be elements of 
.
Adeniran and Solarin (1999) use the term half-Bol to refer to the identity
 |
for a surjective map 
. In their notation,
denotes the image 
, not an integer power. This identity is the left-right
dual of the generalized Bol loop identity,
obtained by reversing the multiplication.
On the other hand, Boerner and Kallaher (1982) use the phrase half-Bol loop to refer to an algebraic loop 
for which one can find a mapping 
such that
 |
Additional conditions on the mapping 
may be imposed (Boerner and Kallaher 1982).
