The algebraic formalism developed in this paper unifies the study of t
he accessibility problem and various notions of feedback linearizabili
ty for discrete-time nonlinear systems. The accessibility problem for
nonlinear discrete-time systems is shown to be easy to tackle by means
of standard linear algebraic tools, whereas this is not the case for
nonlinear continuous-time systems, in which case the most suitable app
roach is provided by differential geometry. The feedback linearization
problem for discrete-time systems is recasted through the language of
differential forms. In the event that a system is not feedback linear
izable, the largest feedback linearizable subsystem is characterized w
ithin the same formalism using the notion of derived flag of a Pfaffia
n system. A discrete-time system may be linearizable by dynamic state
feedback, though it is not linearizable by static state feedback. Nece
ssary and sufficient conditions are given for the existence of a so-ca
lled linearizing output, which in turn is a sufficient condition for d
ynamic state feedback linearizability.