Formal Matrix Rings

  • Piotr KrylovEmail author
  • Askar Tuganbaev
Part of the Algebra and Applications book series (AA, volume 23)


In this chapter, we define formal matrix rings of order 2 and formal matrix rings of arbitrary order n. Their main properties are considered and examples of such rings are given. We indicate the relationship between formal matrix rings, endomorphism rings of modules, and systems of orthogonal idempotents of rings. For formal matrix rings, the Jacobson radical and the prime radical are described. We find when a formal matrix ring is Artinian, Noetherian, regular, unit-regular, and of stable rank 1. In the last section, clean and k-good matrix rings are considered.

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Tomsk State UniversityTomskRussia
  2. 2.National Research University MPEIMoscowRussia

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