论文标题
关于一组长度的系统的无与伦比
On the incomparability of systems of sets of lengths
论文作者
论文摘要
让$ h $是一个有限级组$ g $的krull monoid，以使每个班级都包含一个主要的除数。我们考虑所有长度的$ h $的系统$ \ natcal l（h）$，并在$ \ m nathcal l（h）$包含或包含在系统$ \ Mathcal l（h'）$中的krull monoid $ h'$中的系统$ h'$中，有限类$ g'$ g'$，所有班级和davenport constant $ \ $ \ $ \ $ \ $ \ n d（g）。除其他外，我们表明，如果$ g $要么是订单$ m \ ge 7 $或基本$ 2 $ 2 $ - 等级$ m-1 \ ge 6 $，而$ g'$是任何非同质到$ g $的群体（H'）$无与伦比。
Let $H$ be a Krull monoid with finite class group $G$ such that every class contains a prime divisor. We consider the system $\mathcal L (H)$ of all sets of lengths of $H$ and study when $\mathcal L (H)$ contains or is contained in a system $\mathcal L (H')$ of a Krull monoid $H'$ with finite class group $G'$, prime divisors in all classes and Davenport constant $\mathsf D (G')=\mathsf D (G)$. Among others, we show that if $G$ is either cyclic of order $m \ge 7$ or an elementary $2$-group of rank $m-1 \ge 6$, and $G'$ is any group which is non-isomorphic to $G$ but with Davenport constant $\mathsf D (G')=\mathsf D (G)$, then the systems $\mathcal L (H)$ and $\mathcal L (H')$ are incomparable.
