International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 15, Pages 2373-2387
doi:10.1155/IJMMS.2005.2373

Higher derivations on rings and modules.

Abstract

Let τ be a hereditary torsion theory on ModR and suppose that Qτ:ModR→ModR is the localization functor. It is shown that for all R-modules M, every higher derivation defined on M can be extended uniquely to a higher derivation defined on Qτ(M) if and only if τ is a higher differential torsion theory. It is also shown that if τ is a TTF theory and Cτ:M→M is the colocalization functor, then a higher derivation defined on M can be lifted uniquely to a higher derivation defined on Cτ(M).