Torsion classes and pure subgroups

Barry J. Gardner

Vol. 33 (1970), No. 1, 109–116

DOI: 10.2140/pjm.1970.33.109

Abstract

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

1. If {A_μ|μ ∈ M}⊆𝒯 , then 𝒯 contains the direct sum ΣA_μ.

   For a short exact sequence

   

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