  The main local invariants of a (one variable) differential module over the
complex numbers are given by means of a cyclic basis. In the $p$-adic setting
the existence of a cyclic vector is often unknown. We investigate the existence
of such a cyclic vector in a Banach algebra. We follow the explicit method of
Katz, and we prove the existence of such a cyclic vector under the assumption
that the matrix of the derivation is small enough in norm.

Number Theory