  The magnetoresistivity tensor of an interacting two-dimensional electron
system with a lateral and unidirectional electric or magnetic modulation, in a
perpendicular quantizing magnetic field, is calculated within the Kubo
formalism. The influence of the spin splitting of the Landau bands and of the
density of states (DOS) on the internal structure of the Shubnikov-de Haas
oscillations is analyzed. The Coulomb electron - electron interaction is
responsible for strong screening and exchange effects and is taken into account
in a screened Hartree-Fock approximation, in which the exchange contribution is
calculated self-consistently with the DOS at the Fermi level. This
approximation describes both the exchange enhancement of the spin splitting and
the formation of compressible edge strips, unlike the simpler Hartree and
Hartree-Fock approximations, which yield either the one or the other.
