## Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Tensor-Multinomial Sums of Ideals and Applications

Seminar | October 23 | 5-6 p.m. | 939 Evans Hall

Robert Walker, University of Michigan

Department of Mathematics

Given a polynomial ring $C$ over a field and proper ideals $I$ and $J$ whose generating sets involve disjoint variables, we determine how to embed the associated primes of each power of $I+J$ into a collection of primes described in terms of the associated primes of select powers of $I$ and of $J$. We discuss applications to constructing primary decompositions for powers of $I+J$, and to attacking the persistence problem for associated primes of powers of an ideal. This is joint work with Irena Swanson found on arXiv:1806.03545.

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