A precise result on the arithmetic of non-principal orders in algebraic number fields

2011/04/20 by Philipp, Andreas
#11R27 #13A05 #13F15 #20M13 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1104.3971

Abstract

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.

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