Rings involving idempotents, units and nilpotent elements
  We define the concepts of weakly precious and precious rings which generalize the notions of weakly clean and nil-clean rings. We obtain some fundamental properties of these rings. We also obtain certain subclasses of such rings and then offer new kinds of weakly clean rings and nil-clean rings. 
Nahid Ashrafi, Marjan Sheibani and Huanyin Chen
math.RA