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).

Adeniran, J. O. and Solarin, A. R. T. "A Note on Generalized Bol Identity." An. Stiinţ. Univ. Al. I. Cuza
Iasi. Mat.45, 99-102, 1999.Moorhouse, G. E. "Bol
Loops of Small Order." 2007. http://www.uwyo.edu/moorhouse/pub/bol/.