Restuccia, Gaetana and Matsumura, H. (1992) Integrable derivations II. Accademia Peloritana dei Pericolanti Classe FF.MM.NN., 70. pp. 153-172.
We establish some theorems of strong integrability for derivations of a $k$-algebra $A$ of characteristic $p > O$. After having formally generalized Lipman’s theorem in characteristic $O$, by using differentiations instead of derivations, we extend Lipman’s theorem to rings of characteristic $p > O$, under conditions concerning $A$ ($A$ regular local) and the derivations of $A$. If $A$ is a field, we study the connection between the separability of $A$ over $k$ and the strong integrability of derivations of $A$.
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