ON FLATNESS RELATIVE TO A TORSION THEORY

Abstract

For a torsion radical, σ, σ-flatness (as defined in [8]) is studied. Many of the properties of flat modules are shown to extend and σ-flat modules are characterized under certain restrictions on the associated filter, Lσ. We also define semi-σ-flat modules in a natural way and find conditions equivalent to every R-module being semi-σ-flat.