ABSTRACT
In order to study the ideals of a ring, it is natural to try to decompose arbitrary ideals into special ones which can more easily be investigated. As in the theory of factorization in rings (whose rudiments were developed in section 3), a reasonable theory can be developed only for commutative rings to which we therefore restrict our attention. We start by defining two types of ideals which will play an important role as the smallest building-blocks into which we can decompose arbitrary ideals.
