Ideal Number

A type of number involving the roots of unity which was developed by Kummer while trying to solve Fermat's last theorem. Although factorization over the integers is unique (the fundamental theorem of algebra), factorization is not unique over the complex numbers. Over the ideal numbers, however, factorization in terms of the complex numbers becomes unique. Ideal numbers were so powerful that they were generalized by Dedekind into the more abstract ideals in general rings which are a key part of modern abstract algebra.