勷勤数学•专家报告

题      目：On some Isomorphism Problems

报  告  人：Alfred Geroldinger 教授  (邀请人：袁平之)

                                      University of Graz 格拉茨大学（奥地利）

时      间： 11月18日  14：30-15:30

地     点：数科院东楼401

报告人简介:

        Alfred Geroldinger received a Master Degree in Mathematics from the University of Vienna, a Master Degree in Computer Science from the Vienna University of Technology, and a PhD in Mathematics from the University of Graz. He is a member of the Graz School of Discrete Mathematics and professor at the University of Graz. To date, he has authored/coauthored 130 research articles and coauthored three books.

Non-Unique Factorizations (with F. Halter-Koch), CRC Press, 2006

Combinatorial Number Theory and Additive Group Theory (with I. Ruzsa), Springer 2009

Combinatorial Factorization Theory (with D.J. Grynkiewicz and Q. Zhong), AMS Math. Surveys and Monographs, to appear.

摘      要：

 Let $H$ be a (commutative and cancellative) monoid. If an element $a \in H$ has a factorization $a = u_1 \cdot \ldots \cdot u_k$, where all $u_i$'s are atoms, then $k$ is called a factorization length. The set $\mathsf L (a) \subseteq \mathbb N$ of all factorization lengths is called the length set of $a$, and $\mathcal L (H)=\{\mathsf L (a) \colon a \in H \}$ is the system of length sets of $H$.

Let $H$ be a Krull monoid with class group $G$ and suppose that every class contains a prime divisor. Then $\mathcal L (H) = \mathcal L \big( \mathcal B (G) \big)$, where $\mathcal B (G)$ is the monoid of zero-sum sequences over $G$.  The following two problems are central in the area. Let $G_1$ and $G_2$ be abelian groups.

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