  We show that a semi-commutative Galois extension of a unital associative
algebra can be endowed with the structure of a graded q-differential algebra.
We study the first and higher order noncommutative differential calculus of
semi-commutative Galois extension induced by the graded q-differential algebra.
As an example we consider the quaternions which can be viewed as the
semi-commutative Galois extension of complex numbers.
