Editing Primary decomposition (section)

==Additive theory of ideals==

This result is the first in an area now known as the additive theory of ideals, which studies the ways of representing an ideal as the intersection of a special class of ideals. The decision on the "special class", e.g., primary ideals, is a problem in itself. In the case of non-commutative rings, the class of [[tertiary ideal]]s is a useful substitute for the class of primary ideals.