A algebraic loop 
is a generalized Bol loop if for all elements 
, 
, and 
of 
,
 |
for some map 
. As the name suggests, these are generalizations
of Bol loops; in particular, a Bol loop is a generalized
Bol loop with respect to the identity map 
.
One can show that there is an algebraic duality between generalized Bol loops and algebraic loops which satisfy the half-Bol identity (Adeniran and Solarin 1999).
