The most general way to construct a ring is by specifying generators and relations. Let "F" be a free ring (that is, free algebra over the integers) with the set "X" of symbols, that is, "F" consists of polynomials with integral coefficients in noncommuting variables that are elements of "X". A free ring satisfies the universal property: any function from the set "X" to a ring "R" factors through "F" so that formula_205 is the unique ring homomorphism. Just as in the group case, every ring can be represented as a quotient of a free ring.