The Department of Mathematics & Statistics invites students, faculty, and staff to attend the upcoming colloquium with speaker Dr. Alfred Geroldinger on Monday, July 20th, at 10:00 AM in GSB 308. The talk is entitled On the arithmetic of Krull monoids with torsion class group.
Abstract
Let H be a Krull monoid (e.g. the multiplicative monoid of nonzero elements of a Krull domain). Then every non-invertible element can be factored into irreducible elements. If a = u_1 … u_k with k in N_0 and irreducibles u_1, …, u_k, then k is a factorization length and the set L(a) of all factorization lengths of a is called the length set of a.
The system of length sets is an infinite family of finite subsets of N_0. Its structure depends only on the class group of H and the distribution of prime divisors in the classes. We provide an overview of current knowledge regarding length sets and present new results (joint work with David J. Grynkiewicz and Guoqing Wang) for torsion class groups.
