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In 1843 [[Ernst Kummer|Kummer]] introduced the concept of [[ideal number]], which was developed further by [[Richard Dedekind|Dedekind]] (1876) into the modern theory of [[Ideal (ring theory)|ideals]], special subsets of rings. Multiplication is defined for ideals, and the rings in which they have unique factorization are called [[Dedekind ___domain]]s.
There is a version of [[ordinal arithmetic|unique factorization for ordinals]], though it requires some additional conditions to ensure uniqueness.
==See also==
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