All hereditary torsion theories are differential

AbstractLet α and β be automorphisms on a ring R and δ:R→R an (α,β)-derivation. It is shown that if F is a right Gabriel filter on R then F is δ-invariant if it is both α and β-invariant. A consequence of this result is that every hereditary torsion theory on the category of right R-modules is differential in the sense of Bland (2006). This answers in the affirmative a question posed by Vaš (2007) and strengthens a result due to Golan (1981) on the extendability of a derivation map from a module to its module of quotients at a hereditary torsion theory