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Rings with finite decomposition of identity

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Ukrainian Mathematical Journal Aims and scope

A criterion for semiprime rings with finite decomposition of identity to be prime is given. We also present a brief survey of 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.

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Authors and Affiliations

  1. University of São Paulo, São Paulo, Brazil

    M. A. Dokuchaev

  2. Cze͕stochowa University of Technology, Cze͕stochowa, Poland

    N. M. Gubareni

  3. Shevchenko Kiev National University, Kiev, Ukraine

    V.V. Kirichenko

Authors
  1. M. A. Dokuchaev
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  2. N. M. Gubareni
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  3. V.V. Kirichenko
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 3, pp. 319–340, March, 2011.

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Dokuchaev, M.A., Gubareni, N.M. & Kirichenko, V. Rings with finite decomposition of identity. Ukr Math J 63, 369–392 (2011). https://doi.org/10.1007/s11253-011-0509-9

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  • DOI: https://doi.org/10.1007/s11253-011-0509-9

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