Projective and injective modules

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


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.



Direct Summand Homomorphic Image Projective Module Injective Module Essential Extension 
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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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