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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.
See also Divisor Theory, Fermat's Last Theorem, Ideal