Rings with finite decomposition of identity
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.
English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 3, pp 369-392.
Citation Example: Dokuchaev M. A., Gubareni N. M., Kirichenko V. V. Rings with finite decomposition of identity // Ukr. Mat. Zh. - 2011. - 63, № 3. - pp. 319-340.