Primary decomposition and powers of ideals

Abstract: This talk is about associated primes of powers of an ideal in Noetherian commutative rings. Brodmann proved that the set of associated primes stabilizes for large powers. In general, the number of associated primes can go up or down as the exponent 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 $a_n$. This is a report on my work with Sarah Weinstein, with Jesse Kim and ongoing work with Roswitha Rissner.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

Series comments: Note: To get meeting ID,fill the Google form on the web-site of the series sites.google.com/view/virtual-comm-algebra-seminar/home