Abstract:

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. Copyright 2001 Academic Press.

Language: English

Document Type: Research article

Affiliations: Department of Mathematics, North Dakota State University, Fargo, North Dakota, 58105-5075: