  We generalize the theory of logarithmic derivations through a self-contained
study of modules here dubbed tangential idealizers. We establish reflexiveness
criteria for such modules, provided the ring is a factorial domain. As a main
consequence, necessary e sufficient conditions for their freeness are derived
and the class of tangentially free ideals is introduced, thus extending
(algebraically) the theory of free divisors proposed by K. Saito around 30
years ago.
