The term Bol loop refers to either of two classes of algebraic loops satisfying the so-called Bol identities. In particular, a left Bol loop
is an algebraic loop which, for all , ,
and in , satisfies the left Bol relation

Similarly,
is a right Bol loop provided it satisfies the right Bol relation

Some sources use the term Bol loop to refer to a right Bol loop, whereas some reserve the term for algebraic loops that are Moufang.

Although (left and right) Bol loops have relatively weak structural properties, one can show that such structures
are power associative. Thus, given an
algebraic loop , the element is well-defined for
all elements
and all integers independent of which order the multiplications are performed.

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/.