The algebraic identification method is defined for discrete-time dynamic systems. The extension of the algebraic approach for parameter identification to this ubiquitous class of systems is also based on the module-theoretic vision of discrete-time linear dynamics, which has become a classic. As in the continuous-time case, we achieve closed-loop identification in a relatively small time interval involving few samples and with no need for the probabilistic approach. Several physically oriented case studies of linear and nonlinear nature, as well as mono-variable and multi-variable cases, are discussed in detail along with their corresponding computer simulations.