Additive unit representations in global fields - A survey
  We give an overview on recent results concerning additive unit representations. Furthermore the solutions of some open questions are included. The central problem is whether and how certain rings are (additively) generated by their units. This has been investigated for several types of rings related to global fields, most importantly rings of algebraic integers. We also state some open problems and conjectures which we consider to be important in this field. 
Fabrizio Barroero, Christopher Frei, Robert F. Tichy
math.NT math.RA