x_{1} is a binary operator in structure x_{2} which exhibits the Jacobi property with respect to binary operator x_{3} (which also endows x_{2}) and element/object x_{4} (which is an element of the underlying set which form x_{2}).

This word uses a classifier which involves experimental gismu "socni" as a veljvo. Let x_{1} be denoted by "f", x_{2} be denoted by "X", x_{3} be denoted by "+", and x_{4} be denoted by "e". Then f exhibits the Jacobi property iff, for any x, y, z in X, the following is true: f(x, f(y, z)) + f(z, f(x, y)) + f(y, f(z, x)) = e. Notice that f may not be commutative; it may be necessary to further specify that e is the identity element in X for operstor '+', assuming that such is appropriate.