Daniel Smertnig, University of Graz
“Non-unique factorizations in maximal orders and beyond”
In a Noetherian ring every non-zero-divisor can be written as a product of irreducibles. However, such a representation is usually far from unique. In factorization theory one studies arithmetical invariants describing this non-uniqueness. This has a long tradition in commu- tative settings (in particular in Dedekind domains, Krull monoids), where transfer homomor- phisms often allow one to reduce problems about factorizations to combinatorial problems over abelian groups. This machinery has recently been extendeded to some classes of non- commutative rings. In particular, such transfer homomorphisms exist for maximal orders in central simple algebras over global fields (or more generally, bounded HNP rings) satisfying some additional conditions.
We give a short introduction to factorization theory, illustrate how factorization theoret- ical problems reduce to combinatorial ones, and give an overview over transfer results for noncommutative rings.
MC 5417