Higher derivations on rings and modules

Abstract

Letτbe a hereditary torsion theory onModRand suppose thatQτ:ModR→ModRis the localization functor. It is shown that for allR-modulesM, every higher derivation defined onMcan be extended uniquely to a higher derivation defined onQτ(M)if and only ifτis a higher differential torsion theory. It is also shown that ifτis a TTF theory andCτ:M→Mis the colocalization functor, then a higher derivation defined onMcan be lifted uniquely to a higher derivation defined onCτ(M).