Algebrization of planar vector fields

Abstract

We give a method to determine when a planar vector Field admits an associative and commutative algebra A with unit, for which F is A-algebrizable (Lorch-diferentiable with respect to A). We introduce the quasi-algebrizablevector fields, which are those vector fields F for which there exist scalar functions a, which we call algebrizing factors, in such a way that the products aF are algebrizable vector Fi elds. We give conditions under which a planar vector field is quasi-algebrizable and the algebrizing factor and the inverse integrating factor are found.