Another definition of the GCD is helpful in advanced mathematics, particularly ring theory. The greatest common divisor "g"  of two nonzero numbers "a" and "b" is also their smallest positive integral linear combination, that is, the smallest positive number of the form "ua" + "vb" where "u" and "v" are integers. The set of all integral linear combinations of "a" and "b" is actually the same as the set of all multiples of "g" ("mg", where "m" is an integer). In modern mathematical language, the ideal generated by "a" and "b" is the ideal generated by "g" alone (an ideal generated by a single element is called a principal ideal, and all ideals of the integers are principal ideals). Some properties of the GCD are in fact easier to see with this description, for instance the fact that any common divisor of "a" and "b" also divides the GCD (it divides both terms of "ua" + "vb"). The equivalence of this GCD definition with the other definitions is described below.