Therefore, the set of all numbers "ua" + "vb" is equivalent to the set of multiples "m" of "g". In other words, the set of all possible sums of integer multiples of two numbers ("a" and "b") is equivalent to the set of multiples of gcd("a", "b"). The GCD is said to be the generator of the ideal of "a" and "b". This GCD definition led to the modern abstract algebraic concepts of a principal ideal (an ideal generated by a single element) and a principal ideal domain (a domain in which every ideal is a principal ideal).