Predicted decay ideals

Abstract

For arbitrary positive integers $q_1\ge q_2\ge \cdots$ we construct a family of monomial ideals such that for each positive integer e and for each ideal I in the family, the number of associated primes of I^e is q_e. We present the associated primes explicitly.

Keywords:

• Primary decomposition
• powers of ideals
• associated primes
• monomial ideals

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 13A15
• 13F20