We construct noncommutative multidimensional versions of overconvergent power series
rings and Robba rings. We show that the category of etale (phi, Gamma)-modules over
certain completions of these rings is equivalent to the category of etale (phi, Gamma)-modules
over classical overconvergent or Robba rings as the case may be (hence also to the
category of p-adic Galois representations of Q(p)). In the case of Robba rings, the
assumption of taleness is not necessary, so there exists a notion of trianguline objects
in this sense.