Pipe string for a drilling rig of a well for the extraction of formation fluids, the pipe string comprising a plurality of pipes (11, 50) connected to each other in succession, said plurality of pipes (11, 50) comprising a plurality of drill pipes and a plurality of pipes for cableless bidirectional data transmission and the continuous circulation of a stabilizing fluid in the well for the extraction of formation fluids, the pipes for cableless bidirectional data transmission and the continuous circulation being positioned along the pipe string between two drill pipes at predetermined intervals of one or more drill pipes, each pipe for cableless bidirectional data transmission and the continuous circulation comprises: - a hollow tubular body which extends in length along a longitudinal direction X and which is configured at the ends for being coupled with respective drill pipes of the pipe string; - a radial valve associated with said hollow tubular body arranged to control the flow of the stabilizing fluid in a substantially radial or transversal direction with respect to the longitudinal direction X, said radial valve being a pressure-tight valve and being connectable to a pumping system of a drilling rig outside said tubular body so as to allow the passage of the stabilizing fluid inside said hollow tubular body generating an inside flow directed towards the bottom of the well; - an axial valve associated with said tubular body arranged to control the flow of the stabilizing fluid along said longitudinal direction X; - a communication module associated with said tubular body comprising: - at least one metal plate (21,22,35) selected from: - a transmitting metal plate; - a receiving metal plate; - a transceiver metal plate; - an electronic processing and control unit configured for processing signals to be transmitted by means of said at least one metal plate (21, 35) or signals received by means of said at least one metal plate (22, 35); wherein said communication module is configurable for acting as signal transmitter or signal receiver, or signal repeater or signal regenerator; - one or more supply batteries for feeding said metal plates (21, 22, 35) and said electronic processing and control unit; wherein the transmission of said signals to be transmitted takes place by injecting into a formation fluid surrounding the pipe string, from said at least one metal plate (21, 35), an electric current carrying an information signal, said signals being transmitted between said communication module and a consecutive communication module of a subsequent pipe for cableless bidirectional data transmission and the continuous circulation that is positioned at pre-established intervals of one or more drill pipes. - a hollow tubular body which extends in length along a longitudinal direction X and which is configured at the ends for being coupled with respective drill pipes of the pipe string; - a radial valve associated with said hollow tubular body arranged to control the flow of the stabilizing fluid in a substantially radial or transversal direction with respect to the longitudinal direction X, said radial valve being a pressure-tight valve and being connectable to a pumping system of a drilling rig outside said tubular body so as to allow the passage of the stabilizing fluid inside said hollow tubular body generating an inside flow directed towards the bottom of the well; - an axial valve associated with said tubular body arranged to control the flow of the stabilizing fluid along said longitudinal direction X; - a communication module associated with said tubular body comprising: - at least one metal plate (21,22,35) selected from: - a transmitting metal plate; - a receiving metal plate; - a transceiver metal plate; - an electronic processing and control unit configured for processing signals to be transmitted by means of said at least one metal plate (21, 35) or signals received by means of said at least one metal plate (22, 35); - at least one metal plate (21,22,35) selected from: - a transmitting metal plate; - a receiving metal plate; - a transceiver metal plate; - a transmitting metal plate; - a receiving metal plate; - a transceiver metal plate; - an electronic processing and control unit configured for processing signals to be transmitted by means of said at least one metal plate (21, 35) or signals received by means of said at least one metal plate (22, 35); - one or more supply batteries for feeding said metal plates (21, 22, 35) and said electronic processing and control unit;