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<i>Context. <i/>The poorly-ionized interior of the protoplanetary disk or “dead zone” is the location where dust coagulation processes may be most efficient. However even here, planetesimal formation may be limited by the loss of solid material through radial drift, and by collisional fragmentation of the particles. Both depend on the turbulent properties of the gas.<i>Aims. <i/>Our aim here is to investigate the possibility that solid particles are trapped at local pressure maxima in the dynamically evolving disk. We perform the first 3-D global non-ideal magnetohydrodynamical (MHD) calculations of a section of the disk treating the turbulence driven by the magneto-rotational instability (MRI).<i>Methods. <i/>We use the ZeusMP code with a fixed Ohmic resistivity distribution. The domain contains an inner MRI-active region near the young star and an outer midplane dead zone, with the transition between the two modeled by a sharp increase in the magnetic diffusivity.<i>Results. <i/>The azimuthal magnetic fields generated in the active zone oscillate over time, changing sign about every 150 years. We thus observe the radial structure of the “butterfly pattern” seen previously in local shearing-box simulations. The mean magnetic field diffuses from the active zone into the dead zone, where the Reynolds stress nevertheless dominates, giving a residual <i>α<i/> between 10<sup>-4<sup/> and 10<sup>-3<sup/>. The greater total accretion stress in the active zone leads to a net reduction in the surface density, so that after 800 years an approximate steady state is reached in which a local radial maximum in the midplane pressure lies near the transition radius. We also observe the formation of density ridges within the active zone.<i>Conclusions. <i/>The dead zone in our models possesses a mean magnetic field, significant Reynolds stresses and a steady local pressure maximum at the inner edge, where the outward migration of planetary embryos and the efficient trapping of solid material are possible.