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Self-injective and skew-injective rings

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

Abstract

For a ring A, the following assertions hold.
  1. (1)

    If A is a right p-injective ring with the maximum condition on right annihilators, then A is semiprimary.

     
  2. (2)

    If A is a right self-injective ring, then ℓ(A1 ⋂A2) = ℓA1) + ℓ(A2) for any right ideals A1 A2 of A.

     
  3. (3)

    If A is a right self-injective ring, then ℓ(r(B)) = B for any finitely generated left ideal B of A.

     
  4. (4)

    If A is a right self-injective ring with the maximum condition on left annihilators, then A is a left Artinian ring with the maximum condition on right annihilators.

     

Keywords

Prime Ideal Division Ring Regular Ring Artinian Ring Factor Ring 
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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