THE σ-PURE INJECTIVE BULL, FOR A TORSION RADICAL, σ

Abstract

For a torsion radical σ ([16]) σ-purity, which was defined by Harui and Teply in [12], is given a projective characterization. It is shown to define a pure theory in the sense of Fieldhouse ([5]). σ-pure injective modules are defined and it is shown that, under the condition that every ideal in the associated filter L is finitely generated, every R-module may be embedded as a σ-pure submodule, in a σ-pure injective module. This module, the σ-pure injective hull, is also shown to be unique up to isomorphism.