International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 15, Pages 2373-2387
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 Paul E. Bland. 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.
Let be a hereditary torsion theory on and suppose that is the localization functor. It is shown that for all -modules , every higher derivation defined on can be extended uniquely to a higher derivation defined on if and only if is a higher differential torsion theory. It is also shown that if is a TTF theory and is the colocalization functor, then a higher derivation defined on can be lifted uniquely to a higher derivation defined on .