Arithmetic of non-principal orders in algebraic number fields

Philipp, Andreas

Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 99-102.

Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.

Classification : 11R27, 13A05, 13F15, 20M13
Mots clés : non-unique factorizations, half-factoriality, non-principal orders, algebraic number fields

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