0908.0911Aug 6, 2009This submission has been withdrawn as it is subsumed by (and divided into) the following published papers: "Cleto B. Miranda-Neto, Tangential idealizers and differential ideals, Collect. Math. 67, 311-328, 2016", and "Cleto B. Miranda-Neto, Free logarithmic derivation modules over factorial domains, Math. Res. Lett. 24(1), 153-172, 2017"

Theory of tangential idealizers and tangentially free ideals

Cleto B. Miranda Neto

Commutative Algebra Algebraic Geometry

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Abstract

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.

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