Vol. 31, No. 2, 1969

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Quasi-injective modules and stable torsion classes

Efraim Pacillas Armendariz

Vol. 31 (1969), No. 2, 277–280

In this note we examine the 𝒯 -torsion submodule of quasi-injective R-modules, R a ring with unit, where 𝒯 is a torsion class in the sense of S. E. Dickson. We show that for a stable torsion class 𝒯 , the 𝒯 -torsion submodule of any quasi-injective module is a direct summand, while if 𝒯 contains all Goldie-torsion modules, then every epimorphic image of a quasi-injective module has its 𝒯 -torsion submodule as a direct summand. In addition, we show that for a stable torsion class 𝒯, all 𝒯 -torsion-free modules are injective if and only if R = T(R) K (ring direct sum), with K Artinian semisimple.

Mathematical Subject Classification
Primary: 16.40
Received: 7 October 1968
Published: 1 November 1969
Efraim Pacillas Armendariz