An algebraic loop is a Moufang loop if all triples of elements , , and in satisfy the Moufang identities, i.e., if
1. ,
2. ,
3. , and
4. .
One can show that an algebraic loop which satisfies both the left and right Bol identities is Moufang.
This entry contributed by Christopher Stover
More things to try:
Stover, Christopher. "Moufang Loop." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/MoufangLoop.html
is a Moufang loop if all triples of elements 
, 
,
and 
in 
satisfy the Moufang identities,
i.e., if
,
,
, and
.
which satisfies both the left and right Bol identities is
Moufang.
