Mon, February 21, 2022
4:00 pm - 5:00 pm
Zoom
Speaker: Alfred Geroldinger (University of Graz)
Title: Factorization In Rings, Decompositions Of Modules, And The Interplay With Additive Combinatorics
Abstract: This talk offers a survey of Krull domains and monoids. Krull monoids have a transfer homomorphism onto monoids of zero-sum sequences. The arithmetic of monoids of zero-sum sequences can be studied with methods from additive combinatorics, and transfer homomorphisms allow us to pull them back to Krull monoids. We highlight this interplay and discuss examples of Krull monoids beyond the domain case. At the end, we take a look at transfer Krull monoids and domains (which include classes of non-commutative Dedekind domains).