Vol. 33, No. 1, 1970

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Torsion classes and pure subgroups

Barry J. Gardner

Vol. 33 (1970), No. 1, 109–116
Abstract

In this note we obtain a classification of the classes 𝒯 of abelian groups satisfying the following closure conditions:

  1. If {Aμ|μ M}𝒯 , then 𝒯 contains the direct sum ΣAμ.

    For a short exact sequence

    (∗) 0 → A →  B → C →  0

  2. C ∈𝒯 if B ∈𝒯
  3. B ∈𝒯 if A,C ∈𝒯
  4. A ∈𝒯 if B ∈𝒯 and () is pure.

Mathematical Subject Classification
Primary: 20.30
Milestones
Received: 2 July 1969
Published: 1 April 1970
Authors
Barry J. Gardner