Chapter IV(*)

Associated Prime Ideals and Primary Decomposition

All the rings considered in this chapter are assumed to be commutative and to possess a unit element; all the ring homomorphisms are assumed to map unit element to unit element. By a subring & a ring A we shall mean a subring containing the unit element & A.

Recall that for every A-module E and all x ∈ E, Ann(x) denotes the annihilator of x, the set & a ∈ A such that ax = 0.