Abstract
We prove that every perfect torsion theory for a ring
R
is differential (in the sense of [P. E. Bland, Differential torsion theory, Journal of Pure and Applied Algebra 204 (2006) 1 -- 8]). In this case, we construct the extension of a derivation of a right
R
-module
M
to a derivation of the module of quotients of
M
. Then, we prove that the Lambek and Goldie torsion theories for any
R
are differential.