Rings with finite decomposition of identity - Dokuchaev, M. A.; Gubareni, N. M.; Kirichenko, V. V. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
A criterion for semiprime rings with finite decomposition of identity to be prime is given. We also give a short survey on some finiteness conditions related to the decomposition of identity. We consider the notion of a net of a ring and show that the lattice of all two-sided ideals of a right semidistributive semiperfect ring is distributive. An application of decompositions of identity to groups of units is given.