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

Higher derivations on rings and modules

Department of Mathematics, Eastern Kentucky University, Richmond 40475, KY, USA

Received 27 June 2001; Revised 14 July 2005

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let τ be a hereditary torsion theory on ModR and suppose that Qτ:ModRModR 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:MM is the colocalization functor, then a higher derivation defined on M can be lifted uniquely to a higher derivation defined on Cτ(M).