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Projective and injective modules

  • Askar A. Tuganbaev
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 449)

Abstract

For a ring A, the following conditions are equivalent.
  1. (1)

    All right A-modules are free.

     
  2. (2)

    There exists a simple free module MA.

     
  3. (3)

    AA is a simple module.

     
  4. (4)

    All nonzero elements of A are right mvertible.

     
  5. (5)

    A is a division ring.

     

Keywords

Direct Summand Homomorphic Image Projective Module Injective Module Essential Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Askar A. Tuganbaev
    • 1
  1. 1.Moscow Power Engineering InstituteTechnological UniversityMoscowRussia

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