Additive unit representations in rings over global fields - A survey

作者：Barroero Fabrizio^*; Frei Christopher; Tichy Robert F

来源：Publicationes Mathematicae-Debrecen, 2011, 79(3-4): 291-307.

DOI：10.5486/PMD.2011.5126

• global fields
• sums of units
• unit sum number
• additive unit representations

We give an overview on recent results concerning additive unit representations. Furthermore the solutions of some open questions are included. We focus on rings of integers in number fields and in function fields of one variable over perfect fields. The central problem is whether and how certain rings are (additively) generated by their units. In the final section we deal with matrix rings over quaternions and over Dedekind domains. Our point of view is number-theoretic whereas we do not discuss the general algebraic background.

• 出版日期2011