# Integrable derivations in rings of characteristic $p>0$

Bonazinga, V. (1992) Integrable derivations in rings of characteristic $p>0$. Accademia Peloritana dei Pericolanti Classe FF.MM.NN., 70. pp. 101-117.

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We study the strong integrability of a $\kappa-$algebra $_A$ separable over $\kappa$ where $\kappa$ is a field of characteristic $p> O$. If $-A$ is a field, we state necessary and sufficiet conditions so that a finite number of derivations of $_A$ be strongly integrable. If $_A$ is a local $k$-algebra, one proves the strong integrability of a derivation $_D$ of $_A$ with $D^p = O$ and such that $_D(x) \ \in U(A)$, for some $x \in A, U(A) =units$ of $A$. Finally, we give some positive results in the case of $D(x) \not\in U(A)$, for every $x \in A$.