Half-factorial domains in quadratic fields (Q5925838)

An atomic domain is called half-factorial if any two factorizations into irreducible elements have the same number of factors. Half-factorial orders in quadratic number fields were characterized by the reviewer [\textit{F. Halter-Koch}, Factorization of algebraic integers, Ber. Math.-Stat. Sekt. Forsch. Graz 191 (1983; Zbl 0506.12005)]. In the present paper, the author proves several properties of half-factorial quadratic orders and characterizes them by their normsets (if \(R\) is a quadratic order, then the multiplicative monoid \(\{|\mathcal N (a)|\mid a\in R\} \subset \mathbb N\) is called the normset of \(R\)).