论文标题
Cohen-Macaulay类型的订单，发电机和理想类
Cohen-Macaulay type of orders, generators and ideal classes
论文作者
论文摘要
在本文中，我们研究了埃塔莱代数的Dedekind域（Cohen-Macaulay）类型的订单。我们为类型提供界限，并提供公式来计算它。我们将给定秩序的溢价类型与其分数理想的最小生成集的大小联系起来，从而概括了Gorenstein和Bass Orders的已知结果。最后，我们将带有类型$ 2 $的Multiplicator环提供了一个理想类的分类，并将其用于整体矩阵的共轭类别的计算和Abelian品种在有限字段上的同构类别。
In this paper we study the (Cohen-Macaulay) type of orders over Dedekind domains in étale algebras. We provide a bound for the type, and give formulas to compute it. We relate the type of the overorders of a given order to the size of minimal generating sets of its fractional ideals, generalizing known results for Gorenstein and Bass orders. Finally, we give a classification of the ideal classes with multiplicator ring of type $2$, with applications to the computations of the conjugacy classes of integral matrices and the isomorphism classes of abelian varieties over finite fields.
