  Discrete and q-difference deformations of the structure constants for a class
of associative noncommutative algebras are studied. It is shown that these
deformations are governed by a central system of discrete or q-difference
equations which in particular cases represent discrete and q-difference
versions of the oriented associativity equation. It is demonstrated also that
the celebrated Hirota-Miwa bilinear equation for the AKP and BKP hierarchies
describes discrete deformations of certain finite-dimensional algebras.
