We discuss when an order in a Dedekind domain \(R\) is equal to \(R\) (is the maximal order in \(R\)). Every order in \(R\) is a subring of \(R\). This fact implies the existence of natural homomorphisms between objects related to orders such that the group of Cartier divisors, the Picard group, the group of Weil divisors, the Chow group and the Witt ring of an order. We examine the maximality of an order in \(R\) in the context of such natural homomorphisms.

In [8], we discuss when an order \(\mathcal{O}\) in \(R\) is equal to \(R\) on the assumption that either the Picard group of \(R\) or the Picard group of \(\mathcal{O}\) is a torsion group. In this paper, we abandon this assumption. We formulate equivalent conditions for the maximality of \(\mathcal{O}\) for any Dedekind domain \(R\) and any order \(\mathcal{O}\) in \(R\).

当在戴德域的顺序，我们讨论\（R \）等于\（R \） （是最大为了\（R \） ）。在每一个顺序\（R \）是子环\（R \） 。这一事实意味着与阶相关的对象之间存在自然同态，例如一个阶的 Cartier 因数群、Picard 群、Weil 因数群、Chow 群和 Witt 环。我们在这种自然同态的上下文中检查\(R\)中阶数的极大值。

[8]中，我们将讨论当订单\（\ mathcal {ö} \）在\（R \）等于\（R \）在假定任一皮卡德组的\（R \）或皮卡德的组\（\ mathcal {ö} \）是扭转基。在本文中，我们放弃了这个假设。我们制定等价条件的极大性\（\ mathcal {ö} \）对于任何的Dedekind域\（R \）和任何顺序\（\ mathcal {ö} \）在\（R \） 。