Systems of integrable derivations

Abstract

Let A be a commutative k-algebra, with k a subring of A. We give the definition of n-dimensional differentiation of A over k which formally extends the known one of unidimensional differentiation and we study the group of all n-dimensional differentiation of A over k. In the second part of the work we give some theorems of strong integrability for systems of derivations in terms of n-dimensional differentiation.