Rings with finite decomposition of identity

  • M. A. Dokuchaev Univ. Sao Paulo, Brazil
  • N. M. Gubareni Techn. Univ. Czestochowa, Poland
  • V. V. Kirichenko


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.
How to Cite
Dokuchaev, M. A., N. M. Gubareni, and V. V. Kirichenko. “Rings With Finite Decomposition of Identity”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 3, Mar. 2011, pp. 319-40, https://umj.imath.kiev.ua/index.php/umj/article/view/2719.
Research articles