Numbers of associated primes of powers of ideals

Abstract: This talk is about associated primes of powers of ideals in Noetherian commutative rings. By a result of Brodmann, for any ideal $I$ in a ring $R$, the set of associated primes of $I^n$ stabilizes for large $n$. In general, the number of associated primes can go up or down as $n$ increases. This talk is about sequences $\{a_n\}$ for which there exists an ideal $I$ in a Noetherian commutative ring $R$ such that the number of associated primes of $R/I^n$ is $a_n$. A family of examples shows that $I$ may be prime and the number of associated primes of $I^2$ need not be polynomial in the dimension of the ring.

This is a report on four separate projects with Sarah Weinstein, Jesse Kim, Robert Walker, and ongoing work with Roswitha Rissner.

commutative algebra

Audience: researchers in the topic

Fellowship of the Ring

Series comments: Description: National Commutative Algebra Seminar

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