Half-Factorial Domains in Quadratic Fields

In this paper, we give a norm-theoretic proof of the characterization of HFDs that appear as orders in quadratic fields. The original characterization of orders that are HFDs in quadratic fields is due to F. Halter-Koch (1983, Ber. Mat. Stat. Sektion Forschung.191). Our approach will pay special attention to the normset of such HFDs, and we will give a characterization that relates to the generalized class number of such an order. Additionally, it will be shown that such HFDs are characterized by the factorization properties of their normsets.