A generalized Bol loop is an algebraic loop 
for which some fixed surjective map 
satisfies
 |
for all elements 
, 
, and 
of 
. As the name suggests, these are generalizations of right
Bol loops; in particular, a right 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).
