| Abstract: | ABSTRACT Let R be a Noetherian ring and M a finitely generated R -module. In this article, we introduce the set of prime ideals Fnd M , the foundation primes of M . Using the fact that this set is nicely organized by foundation levels, we present an approach to the problem of understanding Annspec M , the annihilator primes of M , via Fnd M . We show: (1) Fnd M is a finite set containing Annspec M . Further, suppose that moreover every ideal of R has a centralizing sequence of generators; now, Annspec M is equal to the set Ass M of associated primes of M. Then: (2) For an arbitrary P ∈ Fnd M , P ∈ Annspec M if and only if there is no Q ∈ Annspec M such that P contains Q , and at the same time, the minimal foundation level on which appears P is greater than the minimal foundation level on which appears Q . |
